MinT - Best Known (31, 31+65, s)-Nets in Base 32

Best Known (31, 31+65, s)-Nets in Base 32

(31, 31+65, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 96, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 96, 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+65, 192)-Net in Base 32 — Constructive

(31, 96, 192)-net in base 32, using

2 times m-reduction [i] based on (31, 98, 192)-net in base 32, using
- base change [i] based on digital (3, 70, 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]

(31, 31+65, 273)-Net over F₃₂ — Digital

Digital (31, 96, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 96, 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+65, 12115)-Net in Base 32 — Upper bound on s

There is no (31, 96, 12116)-net in base 32, because

1 times m-reduction [i] would yield (31, 95, 12116)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97688 496044 234305 088118 534351 900802 339656 645351 764700 789086 460890 953062 976991 705931 475511 725186 688711 796778 397523 721565 492117 526573 860663 829450 > 32⁹⁵ [i]