MinT - Best Known (90−34, 90, s)-Nets in Base 32

Best Known (90−34, 90, s)-Nets in Base 32

(90−34, 90, 324)-Net over F₃₂ — Constructive and digital

Digital (56, 90, 324)-net over F₃₂, using

1 times m-reduction [i] based on digital (56, 91, 324)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 11, 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 (3, 14, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂ (see above)
  3. digital (7, 24, 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]
  4. digital (7, 42, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(90−34, 90, 546)-Net in Base 32 — Constructive

(56, 90, 546)-net in base 32, using

base change [i] based on (41, 75, 546)-net in base 64, using
- (u,Â u+v)-construction [i] based on
  1. (7, 24, 258)-net in base 64, using
    - base change [i] based on digital (1, 18, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. (17, 51, 288)-net in base 64, using
    - 5 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
      - base change [i] based on digital (9, 48, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(90−34, 90, 5423)-Net over F₃₂ — Digital

Digital (56, 90, 5423)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−34, 90, large)-Net in Base 32 — Upper bound on s

There is no (56, 90, large)-net in base 32, because

32 times m-reduction [i] would yield (56, 58, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]