MinT - Best Known (31, 31+67, s)-Nets in Base 32

Best Known (31, 31+67, s)-Nets in Base 32

(31, 31+67, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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+67, 192)-Net in Base 32 — Constructive

(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+67, 273)-Net over F₃₂ — Digital

Digital (31, 98, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 98, 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+67, 11260)-Net in Base 32 — Upper bound on s

There is no (31, 98, 11261)-net in base 32, because

1 times m-reduction [i] would yield (31, 97, 11261)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 996335 647271 122606 801522 549687 773796 437406 385371 249479 541498 414111 622550 428340 315908 577363 026462 583974 483155 893408 871379 592421 510875 244660 814084 > 32⁹⁷ [i]