MinT - Best Known (106−43, 106, s)-Nets in Base 32

Best Known (106−43, 106, s)-Nets in Base 32

(106−43, 106, 322)-Net over F₃₂ — Constructive and digital

Digital (63, 106, 322)-net over F₃₂, using

1 times m-reduction [i] based on digital (63, 107, 322)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 21, 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, 31, 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, 55, 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]

(106−43, 106, 515)-Net in Base 32 — Constructive

(63, 106, 515)-net in base 32, using

32² times duplication [i] based on (61, 104, 515)-net in base 32, using
- base change [i] based on digital (22, 65, 515)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 21, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
    2. digital (1, 44, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(106−43, 106, 3372)-Net over F₃₂ — Digital

Digital (63, 106, 3372)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−43, 106, large)-Net in Base 32 — Upper bound on s

There is no (63, 106, large)-net in base 32, because

41 times m-reduction [i] would yield (63, 65, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]