MinT - Best Known (95−37, 95, s)-Nets in Base 27

Best Known (95−37, 95, s)-Nets in Base 27

(95−37, 95, 274)-Net over F₂₇ — Constructive and digital

Digital (58, 95, 274)-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 (4, 22, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
4. digital (7, 44, 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]

(95−37, 95, 452)-Net in Base 27 — Constructive

(58, 95, 452)-net in base 27, using

(u,Â u+v)-construction [i] based on
1. (6, 24, 82)-net in base 27, using
  - base change [i] based on digital (0, 18, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
2. (34, 71, 370)-net in base 27, using
  - 1 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
    - base change [i] based on digital (16, 54, 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]

(95−37, 95, 3306)-Net over F₂₇ — Digital

Digital (58, 95, 3306)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−37, 95, large)-Net in Base 27 — Upper bound on s

There is no (58, 95, large)-net in base 27, because

35 times m-reduction [i] would yield (58, 60, large)-net in base 27, but
- mutually orthogonal hypercube bound [i]