MinT - Best Known (57, 57+37, s)-Nets in Base 32

Best Known (57, 57+37, s)-Nets in Base 32

(57, 57+37, 322)-Net over F₃₂ — Constructive and digital

Digital (57, 94, 322)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 19, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (9, 27, 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]
3. digital (11, 48, 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]

(57, 57+37, 517)-Net in Base 32 — Constructive

(57, 94, 517)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (13, 31, 258)-net in base 32, using
  - 1 times m-reduction [i] based on (13, 32, 258)-net in base 32, using
    - base change [i] based on digital (1, 20, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (26, 63, 259)-net in base 32, using
  - 1 times m-reduction [i] based on (26, 64, 259)-net in base 32, using
    - base change [i] based on digital (2, 40, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(57, 57+37, 3940)-Net over F₃₂ — Digital

Digital (57, 94, 3940)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+37, large)-Net in Base 32 — Upper bound on s

There is no (57, 94, large)-net in base 32, because

35 times m-reduction [i] would yield (57, 59, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]