MinT - Best Known (51, 51+33, s)-Nets in Base 32

Best Known (51, 51+33, s)-Nets in Base 32

(51, 51+33, 300)-Net over F₃₂ — Constructive and digital

Digital (51, 84, 300)-net over F₃₂, using

2 times m-reduction [i] based on digital (51, 86, 300)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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 (7, 24, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (9, 44, 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]

(51, 51+33, 517)-Net in Base 32 — Constructive

(51, 84, 517)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (12, 28, 258)-net in base 32, using
  - base change [i] based on (4, 20, 258)-net in base 128, using
    - 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
      - base change [i] based on digital (1, 21, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (23, 56, 259)-net in base 32, using
  - base change [i] based on digital (2, 35, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(51, 51+33, 3702)-Net over F₃₂ — Digital

Digital (51, 84, 3702)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+33, large)-Net in Base 32 — Upper bound on s

There is no (51, 84, large)-net in base 32, because

31 times m-reduction [i] would yield (51, 53, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]