MinT - Best Known (26, 77, s)-Nets in Base 32

Best Known (26, 77, s)-Nets in Base 32

Digital (26, 77, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 77, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(26, 77, 192)-net in base 32, using

t-expansion [i] based on (25, 77, 192)-net in base 32, using
- base change [i] based on digital (3, 55, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

Digital (26, 77, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 77, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(26, 77, 257)-net in base 32, using

7 times m-reduction [i] based on (26, 84, 257)-net in base 32, using
- base change [i] based on digital (12, 70, 257)-net over F₆₄, using
  - net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
      - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

There is no (26, 77, 12345)-net in base 32, because

1 times m-reduction [i] would yield (26, 76, 12345)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 465635 269284 952214 891901 934461 512757 068832 686664 926013 939751 685891 886040 188948 139407 947830 725675 264721 422910 440960 > 32⁷⁶ [i]