MinT - Best Known (56−39, 56, s)-Nets in Base 32

Best Known (56−39, 56, s)-Nets in Base 32

(56−39, 56, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 56, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 56, 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]

(56−39, 56, 158)-Net over F₃₂ — Digital

Digital (17, 56, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 56, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(56−39, 56, 177)-Net in Base 32 — Constructive

(17, 56, 177)-net in base 32, using

4 times m-reduction [i] based on (17, 60, 177)-net in base 32, using
- base change [i] based on digital (7, 50, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(56−39, 56, 5809)-Net in Base 32 — Upper bound on s

There is no (17, 56, 5810)-net in base 32, because

1 times m-reduction [i] would yield (17, 55, 5810)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 60779 956580 719066 071431 716903 751934 656348 671963 288218 784020 977830 349975 404878 241680 > 32⁵⁵ [i]