MinT - Best Known (26, 81, s)-Nets in Base 32

Best Known (26, 81, s)-Nets in Base 32

Digital (26, 81, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 81, 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, 81, 177)-net in base 32, using

Digital (26, 81, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 81, 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, 81, 257)-net in base 32, using

3 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, 81, 10143)-net in base 32, because

1 times m-reduction [i] would yield (26, 80, 10143)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 584023 260796 690874 486203 596476 527182 125760 534805 317996 846934 349469 438943 873258 277778 689571 725963 653369 798241 868865 320036 > 32⁸⁰ [i]