MinT - Information on Result #1230053

Information on Result #1230053

Digital (135, 147, 5595852)-net over F₉, using generalized (u,Â u+v)-construction based on

digital (2, 5, 212)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁵, 212, F₉, 3, 3) (dual of [(212, 3), 631, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(9⁵, 212, F₉, 2, 3) (dual of [(212, 2), 419, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁵, 212, F₉, 3) (dual of [212, 207, 4]-code or 212-cap in PG(4,9)), using
      - caps completed using a computer search [i]
digital (7, 11, 3240)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹¹, 3240, F₉, 4, 4) (dual of [(3240, 4), 12949, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(9¹¹, 3240, F₉, 3, 4) (dual of [(3240, 3), 9709, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(9¹¹, 6480, F₉, 4) (dual of [6480, 6469, 5]-code), using
      - base reduction for projective spaces (embedding PG(5,81) in PG(10,9)) [i] based on linear OA(81⁶, 6480, F₈₁, 4) (dual of [6480, 6474, 5]-code), using
        1 times truncation [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
digital (35, 41, 2796200)-net over F₉, using
- s-reduction based on digital (35, 41, 2796201)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁴¹, 2796201, F₉, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(9⁴¹, large, F₉, 6) (dual of [large, large−41, 7]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’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 F₉, using
- net defined by OOA [i] based on linear OOA(9⁹⁰, 2796200, F₉, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(9⁹⁰, 8388601, F₉, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁹⁰, 8388602, F₉, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
      - trace code [i] based on linear OOA(81⁴⁵, 4194301, F₈₁, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁴⁵, 8388602, F₈₁, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁴⁵, large, F₈₁, 12) (dual of [large, large−45, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’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.