MinT - Best Known (108−81, 108, s)-Nets in Base 32

Best Known (108−81, 108, s)-Nets in Base 32

(108−81, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (27, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(108−81, 108, 177)-Net in Base 32 — Constructive

(27, 108, 177)-net in base 32, using

t-expansion [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(108−81, 108, 225)-Net over F₃₂ — Digital

Digital (27, 108, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 108, 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]

(108−81, 108, 5383)-Net in Base 32 — Upper bound on s

There is no (27, 108, 5384)-net in base 32, because

1 times m-reduction [i] would yield (27, 107, 5384)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 113219 613455 973519 684561 042747 153158 306626 386424 935031 956128 865660 697129 315207 733398 345353 735150 743052 133554 431539 612471 432130 852239 855467 389210 292100 832427 463200 > 32¹⁰⁷ [i]