MinT - Information on Result #1229880

Information on Result #1229880

Digital (137, 149, 5597127)-net over F₈, using generalized (u,Â u+v)-construction based on

digital (3, 6, 695)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁶, 695, F₈, 3, 3) (dual of [(695, 3), 2079, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(8⁶, 695, F₈, 2, 3) (dual of [(695, 2), 1384, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁶, 695, F₈, 3) (dual of [695, 689, 4]-code or 695-cap in PG(5,8)), using
      - caps completed using a computer search [i]
digital (8, 12, 4032)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹², 4032, F₈, 4, 4) (dual of [(4032, 4), 16116, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(8¹², 4032, F₈, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
      - trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
        1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
digital (35, 41, 2796200)-net over F₈, using
- s-reduction based on digital (35, 41, 2796201)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8⁴¹, 2796201, F₈, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(8⁴¹, large, F₈, 6) (dual of [large, large−41, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (78, 90, 2796200)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁹⁰, 2796200, F₈, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(8⁹⁰, 8388601, F₈, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁹⁰, 8388602, F₈, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
      - trace code [i] based on linear OOA(64⁴⁵, 4194301, F₆₄, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64⁴⁵, 8388602, F₆₄, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁴⁵, large, F₆₄, 12) (dual of [large, large−45, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.