MinT - Best Known (12, 37, s)-Nets in Base 32

Best Known (12, 37, s)-Nets in Base 32

(12, 37, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 37, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 37, 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, 37, 129)-Net in Base 32 — Constructive

(12, 37, 129)-net in base 32, using

5 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, 37, 129)-Net over F₃₂ — Digital

Digital (12, 37, 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, 37, 133)-Net in Base 32

(12, 37, 133)-net in base 32, using

5 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, 37, 5584)-Net in Base 32 — Upper bound on s

There is no (12, 37, 5585)-net in base 32, because

1 times m-reduction [i] would yield (12, 36, 5585)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 533806 832307 906700 998101 795633 865570 688056 499980 018188 > 32³⁶ [i]