MinT - Best Known (30, 30+50, s)-Nets in Base 32

Best Known (30, 30+50, s)-Nets in Base 32

(30, 30+50, 120)-Net over F₃₂ — Constructive and digital

Digital (30, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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]

(30, 30+50, 257)-Net in Base 32 — Constructive

(30, 80, 257)-net in base 32, using

base change [i] based on digital (0, 50, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(30, 30+50, 273)-Net over F₃₂ — Digital

Digital (30, 80, 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]

(30, 30+50, 21502)-Net in Base 32 — Upper bound on s

There is no (30, 80, 21503)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 584262 019208 419532 048803 278327 057252 422828 154968 369927 741050 973431 990972 369432 792577 155724 951613 819053 901405 571812 293242 > 32⁸⁰ [i]