MinT - Best Known (40−27, 40, s)-Nets in Base 32

Best Known (40−27, 40, s)-Nets in Base 32

(40−27, 40, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 40, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 40, 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]

(40−27, 40, 129)-Net over F₃₂ — Digital

Digital (13, 40, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 40, 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]

(40−27, 40, 150)-Net in Base 32 — Constructive

(13, 40, 150)-net in base 32, using

2 times m-reduction [i] based on (13, 42, 150)-net in base 32, using
- base change [i] based on digital (1, 30, 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]

(40−27, 40, 161)-Net in Base 32

(13, 40, 161)-net in base 32, using

2 times m-reduction [i] based on (13, 42, 161)-net in base 32, using
- base change [i] based on digital (6, 35, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(40−27, 40, 5984)-Net in Base 32 — Upper bound on s

There is no (13, 40, 5985)-net in base 32, because

1 times m-reduction [i] would yield (13, 39, 5985)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 50269 727243 339076 991917 837940 608468 665934 234597 782930 436768 > 32³⁹ [i]