MinT - Best Known (27, 81, s)-Nets in Base 32

Best Known (27, 81, s)-Nets in Base 32

Digital (27, 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]

(27, 81, 192)-net in base 32, using

3 times m-reduction [i] based on (27, 84, 192)-net in base 32, using
- base change [i] based on digital (3, 60, 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 (27, 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]

(27, 81, 257)-net in base 32, using

9 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, 81, 11534)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 82 666805 916620 891233 702690 340543 905350 336924 111759 631672 123553 153709 096095 039439 898936 617828 439190 404636 373907 918105 239712 > 32⁸¹ [i]