MinT - Best Known (4, 4+10, s)-Nets in Base 32

Best Known (4, 4+10, s)-Nets in Base 32

(4, 4+10, 64)-Net over F₃₂ — Constructive and digital

Digital (4, 14, 64)-net over F₃₂, using

t-expansion [i] based on digital (3, 14, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(4, 4+10, 71)-Net over F₃₂ — Digital

Digital (4, 14, 71)-net over F₃₂, using

net from sequence [i] based on digital (4, 70)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 4 and N(F) ≥ 71, using
  - a curve from the manYPoints database [i]

(4, 4+10, 129)-Net in Base 32 — Constructive

(4, 14, 129)-net in base 32, using

base change [i] based on digital (0, 10, 129)-net over F₁₂₈, using
- net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
    - the rational function field F₁₂₈(x) [i]
  - Niederreiter sequence [i]

(4, 4+10, 1374)-Net in Base 32 — Upper bound on s

There is no (4, 14, 1375)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1181 815636 569729 741526 > 32¹⁴ [i]