MinT - Information on Result #1234688

Information on Result #1234688

Digital (34, 44, 3355904)-net over F₂₅₆, using generalized (u,Â u+v)-construction based on

digital (0, 0, 13109)-net over F₂₅₆, using
- s-reduction based on digital (0, 0, s)-net over F₂₅₆ for arbitrarily large s, using
  - arbitrary set of 256⁰ points [i]
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 0, 13109)-net over F₂₅₆ (see above)
digital (0, 1, 13109)-net over F₂₅₆, using
- s-reduction based on digital (0, 1, s)-net over F₂₅₆ for arbitrarily large s, using
  - construction for strength kÂ =Â 1 [i]
digital (0, 1, 13109)-net over F₂₅₆ (see above)
digital (0, 1, 13109)-net over F₂₅₆ (see above)
digital (0, 1, 13109)-net over F₂₅₆ (see above)
digital (0, 1, 13109)-net over F₂₅₆ (see above)
digital (1, 3, 13109)-net over F₂₅₆, using
- s-reduction based on digital (1, 3, 65793)-net over F₂₅₆, using
  - kÂ =Â 2 construction [i]
digital (1, 3, 13109)-net over F₂₅₆ (see above)
digital (1, 4, 13109)-net over F₂₅₆, using
- s-reduction based on digital (1, 4, 65537)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
digital (2, 7, 13109)-net over F₂₅₆, using
- s-reduction based on digital (2, 7, 32640)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256⁷, 32640, F₂₅₆, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
      - a code by Danev and Olsson [i]
digital (12, 22, 13109)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256²², 13109, F₂₅₆, 10, 10) (dual of [(13109, 10), 131068, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(256²², 65545, F₂₅₆, 10) (dual of [65545, 65523, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(256²², 65547, F₂₅₆, 10) (dual of [65547, 65525, 11]-code), using
      - constructionÂ X applied to C_e(9) âŠ‚ C_e(5) [i] based on
        linear OA(256¹⁹, 65536, F₂₅₆, 10) (dual of [65536, 65517, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.