MinT - Best Known (12, 12+29, s)-Nets in Base 32

Best Known (12, 12+29, s)-Nets in Base 32

(12, 12+29, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 41, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 41, 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]

(12, 12+29, 129)-Net in Base 32 — Constructive

(12, 41, 129)-net in base 32, using

1 times m-reduction [i] based on (12, 42, 129)-net in base 32, using
- base change [i] based on digital (0, 30, 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]

(12, 12+29, 129)-Net over F₃₂ — Digital

Digital (12, 41, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(12, 12+29, 133)-Net in Base 32

(12, 41, 133)-net in base 32, using

1 times m-reduction [i] based on (12, 42, 133)-net in base 32, using
- base change [i] based on digital (5, 35, 133)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
      - a curve from the manYPoints database [i]

(12, 12+29, 3888)-Net in Base 32 — Upper bound on s

There is no (12, 41, 3889)-net in base 32, because

1 times m-reduction [i] would yield (12, 40, 3889)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 611538 389715 525439 055236 989457 552146 070017 606709 752784 403976 > 32⁴⁰ [i]