MinT - Best Known (60, 96, s)-Nets in Base 27

Best Known (60, 96, s)-Nets in Base 27

(60, 96, 286)-Net over F₂₇ — Constructive and digital

Digital (60, 96, 286)-net over F₂₇, using

1 times m-reduction [i] based on digital (60, 97, 286)-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 (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]

(60, 96, 730)-Net in Base 27 — Constructive

(60, 96, 730)-net in base 27, using

base change [i] based on digital (36, 72, 730)-net over F₈₁, using
- net from sequence [i] based on digital (36, 729)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 36 and N(F) ≥ 730, using
    - the Hermitian function field over F₈₁ [i]

(60, 96, 4529)-Net over F₂₇ — Digital

Digital (60, 96, 4529)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 96, large)-Net in Base 27 — Upper bound on s

There is no (60, 96, large)-net in base 27, because

34 times m-reduction [i] would yield (60, 62, large)-net in base 27, but
- mutually orthogonal hypercube bound [i]