MinT - Best Known (59, 59+34, s)-Nets in Base 27

Best Known (59, 59+34, s)-Nets in Base 27

(59, 59+34, 298)-Net over F₂₇ — Constructive and digital

Digital (59, 93, 298)-net over F₂₇, using

1 times m-reduction [i] based on digital (59, 94, 298)-net over F₂₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (4, 12, 64)-net over F₂₇, using
    - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
  2. digital (6, 17, 76)-net over F₂₇, using
    - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  3. digital (6, 23, 76)-net over F₂₇, using
    - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)
  4. digital (7, 42, 82)-net over F₂₇, using
    - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
        a function field by SÃ©mirat [i]

(59, 59+34, 486)-Net in Base 27 — Constructive

(59, 93, 486)-net in base 27, using

1 times m-reduction [i] based on (59, 94, 486)-net in base 27, using
- (u,Â u+v)-construction [i] based on
  1. (9, 26, 116)-net in base 27, using
    - 2 times m-reduction [i] based on (9, 28, 116)-net in base 27, using
      - base change [i] based on digital (2, 21, 116)-net over F₈₁, using
        net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
  2. (33, 68, 370)-net in base 27, using
    - base change [i] based on digital (16, 51, 370)-net over F₈₁, using
      - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(59, 59+34, 5489)-Net over F₂₇ — Digital

Digital (59, 93, 5489)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+34, large)-Net in Base 27 — Upper bound on s

There is no (59, 93, large)-net in base 27, because

32 times m-reduction [i] would yield (59, 61, large)-net in base 27, but
- mutually orthogonal hypercube bound [i]