MinT - Information on Result #1226859

Information on Result #1226859

Digital (26, 37, 52509)-net over F₆₄, using (u,Â u+v)-construction based on

digital (1, 6, 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]
digital (20, 31, 52429)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³¹, 52429, F₆₄, 11, 11) (dual of [(52429, 11), 576688, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(64³¹, 262146, F₆₄, 11) (dual of [262146, 262115, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³¹, 262147, F₆₄, 11) (dual of [262147, 262116, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(64³¹, 262144, F₆₄, 11) (dual of [262144, 262113, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(64²⁸, 262144, F₆₄, 10) (dual of [262144, 262116, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.