MinT - Best Known (27, 27+61, s)-Nets in Base 32

Best Known (27, 27+61, s)-Nets in Base 32

Digital (27, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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, 88, 177)-net in base 32, using

Digital (27, 88, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 88, 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, 88, 257)-net in base 32, using

2 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, 88, 8988)-net in base 32, because

1 times m-reduction [i] would yield (27, 87, 8988)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89017 784442 808295 032528 898045 294282 452776 909126 098102 296261 017060 082885 282182 562750 391649 525919 914375 946073 354013 579193 645940 243904 > 32⁸⁷ [i]