MinT - Best Known (14, 49, s)-Nets in Base 32

Best Known (14, 49, s)-Nets in Base 32

(14, 49, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 49, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 49, 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]

(14, 49, 129)-Net in Base 32 — Constructive

(14, 49, 129)-net in base 32, using

base change [i] based on digital (0, 35, 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]

(14, 49, 146)-Net over F₃₂ — Digital

Digital (14, 49, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(14, 49, 4106)-Net in Base 32 — Upper bound on s

There is no (14, 49, 4107)-net in base 32, because

1 times m-reduction [i] would yield (14, 48, 4107)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 767437 982810 814616 863242 465192 547702 780315 249013 533023 475266 166712 061440 > 32⁴⁸ [i]