MinT - Best Known (99−37, 99, s)-Nets in Base 32

Best Known (99−37, 99, s)-Nets in Base 32

(99−37, 99, 348)-Net over F₃₂ — Constructive and digital

Digital (62, 99, 348)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (10, 22, 108)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 7, 44)-net over F₃₂, using
      - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
    2. digital (3, 15, 64)-net over F₃₂, using
      - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
2. digital (11, 29, 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]
3. digital (11, 48, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(99−37, 99, 577)-Net in Base 32 — Constructive

(62, 99, 577)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. digital (3, 21, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. (41, 78, 513)-net in base 32, using
  - base change [i] based on digital (28, 65, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(99−37, 99, 6365)-Net over F₃₂ — Digital

Digital (62, 99, 6365)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−37, 99, large)-Net in Base 32 — Upper bound on s

There is no (62, 99, large)-net in base 32, because

35 times m-reduction [i] would yield (62, 64, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]