MinT - Best Known (27, 89, s)-Nets in Base 32

Best Known (27, 89, s)-Nets in Base 32

Digital (27, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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, 89, 177)-net in base 32, using

Digital (27, 89, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 89, 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, 89, 257)-net in base 32, using

1 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, 89, 8377)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 910502 020875 876197 692444 717739 026853 934808 819583 615745 598063 031468 877957 532611 679118 814731 025206 813888 295952 454832 638459 158997 781792 > 32⁸⁹ [i]