MinT - Best Known (9, 26, s)-Nets in Base 32

Best Known (9, 26, s)-Nets in Base 32

(9, 26, 104)-Net over F₃₂ — Constructive and digital

Digital (9, 26, 104)-net over F₃₂, using

net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by SÃ©mirat [i]

(9, 26, 108)-Net over F₃₂ — Digital

Digital (9, 26, 108)-net over F₃₂, using

net from sequence [i] based on digital (9, 107)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 108, using
  - a curve from the manYPoints database [i]

(9, 26, 150)-Net in Base 32 — Constructive

(9, 26, 150)-net in base 32, using

2 times m-reduction [i] based on (9, 28, 150)-net in base 32, using
- base change [i] based on digital (1, 20, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(9, 26, 6132)-Net in Base 32 — Upper bound on s

There is no (9, 26, 6133)-net in base 32, because

1 times m-reduction [i] would yield (9, 25, 6133)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 42 548545 160866 929800 928201 591193 731134 > 32²⁵ [i]