MinT - Best Known (18−12, 18, s)-Nets in Base 32

Best Known (18−12, 18, s)-Nets in Base 32

(18−12, 18, 76)-Net over F₃₂ — Constructive and digital

Digital (6, 18, 76)-net over F₃₂, using

t-expansion [i] based on digital (5, 18, 76)-net over F₃₂, using
- net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(18−12, 18, 86)-Net over F₃₂ — Digital

Digital (6, 18, 86)-net over F₃₂, using

net from sequence [i] based on digital (6, 85)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 6 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(18−12, 18, 129)-Net in Base 32 — Constructive

(6, 18, 129)-net in base 32, using

3 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on digital (0, 15, 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]

(18−12, 18, 3161)-Net in Base 32 — Upper bound on s

There is no (6, 18, 3162)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1238 303576 808641 431327 664812 > 32¹⁸ [i]