MinT - Information on Result #3266755

Information on Result #3266755

Digital (32, 45, 43771)-net over F₆₄, using 64¹ times duplication based on digital (31, 44, 43771)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (1, 7, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
2. digital (24, 37, 43691)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64³⁷, 43691, F₆₄, 13, 13) (dual of [(43691, 13), 567946, 14]-NRT-code), using
    - OOA 6-folding and stacking with additional row [i] based on linear OA(64³⁷, 262147, F₆₄, 13) (dual of [262147, 262110, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(64³⁷, 262144, F₆₄, 13) (dual of [262144, 262107, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.