MinT - Best Known (27, 75, s)-Nets in Base 32

Best Known (27, 75, s)-Nets in Base 32

Digital (27, 75, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 75, 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]

(27, 75, 216)-net in base 32, using

2 times m-reduction [i] based on (27, 77, 216)-net in base 32, using
- base change [i] based on digital (5, 55, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

Digital (27, 75, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 75, 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]

(27, 75, 257)-net in base 32, using

15 times m-reduction [i] based on (27, 90, 257)-net in base 32, using
- base change [i] based on digital (12, 75, 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 (27, 75, 15969)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 77027 765090 588457 821248 185392 859596 863871 101314 316368 825384 415758 868422 752707 424217 453358 086185 747319 659744 609924 > 32⁷⁵ [i]