MinT - Information on Result #1227942

Information on Result #1227942

Digital (42, 65, 828)-net over F₈₁, using (u,Â u+v)-construction based on

digital (9, 20, 232)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (2, 7, 3240)-net over F₈₁, using
    - net defined by OOA [i] based on linear OOA(81⁷, 3240, F₈₁, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
  2. digital (2, 13, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
digital (22, 45, 596)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁴⁵, 596, F₈₁, 23, 23) (dual of [(596, 23), 13663, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(81⁴⁵, 6557, F₈₁, 23) (dual of [6557, 6512, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁴⁵, 6561, F₈₁, 23) (dual of [6561, 6516, 24]-code), using
      - an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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.