MinT - Best Known (59, 96, s)-Nets in Base 27

Best Known (59, 96, s)-Nets in Base 27

(59, 96, 280)-Net over F₂₇ — Constructive and digital

Digital (59, 96, 280)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 13, 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 (4, 16, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
3. digital (6, 24, 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]
4. digital (6, 43, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)

(59, 96, 470)-Net in Base 27 — Constructive

(59, 96, 470)-net in base 27, using

base change [i] based on digital (35, 72, 470)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 19, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
  2. digital (16, 53, 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, 96, 3622)-Net over F₂₇ — Digital

Digital (59, 96, 3622)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 96, large)-Net in Base 27 — Upper bound on s

There is no (59, 96, large)-net in base 27, because

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