MinT - Best Known (31, 31+58, s)-Nets in Base 32

Best Known (31, 31+58, s)-Nets in Base 32

(31, 31+58, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 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]

(31, 31+58, 216)-Net in Base 32 — Constructive

(31, 89, 216)-net in base 32, using

2 times m-reduction [i] based on (31, 91, 216)-net in base 32, using
- base change [i] based on digital (5, 65, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(31, 31+58, 273)-Net over F₃₂ — Digital

Digital (31, 89, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 89, 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+58, 15653)-Net in Base 32 — Upper bound on s

There is no (31, 89, 15654)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 91 010833 394144 662014 533224 947225 178809 550351 619716 485600 560219 756917 592848 625897 961732 994708 479582 014568 226961 614018 932410 603837 032076 > 32⁸⁹ [i]