MinT - Best Known (31, 31+74, s)-Nets in Base 32

Best Known (31, 31+74, s)-Nets in Base 32

(31, 31+74, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 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]

(31, 31+74, 177)-Net in Base 32 — Constructive

(31, 105, 177)-net in base 32, using

t-expansion [i] based on (25, 105, 177)-net in base 32, using
- 3 times m-reduction [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]

(31, 31+74, 273)-Net over F₃₂ — Digital

Digital (31, 105, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 105, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(31, 31+74, 8810)-Net in Base 32 — Upper bound on s

There is no (31, 105, 8811)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 110 287866 932043 650113 447936 452575 085595 644552 115551 657837 556711 940586 815545 379469 597307 497775 880529 183727 739516 286493 413901 155508 382739 476887 319995 653680 030348 > 32¹⁰⁵ [i]