MinT - Best Known (60, 60+34, s)-Nets in Base 27

Best Known (60, 60+34, s)-Nets in Base 27

(60, 60+34, 304)-Net over F₂₇ — Constructive and digital

Digital (60, 94, 304)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (2, 8, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]
2. 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]
3. digital (4, 15, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
4. digital (4, 21, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)
5. digital (4, 38, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇ (see above)

(60, 60+34, 730)-Net in Base 27 — Constructive

(60, 94, 730)-net in base 27, using

2 times m-reduction [i] based on (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, 60+34, 6064)-Net over F₂₇ — Digital

Digital (60, 94, 6064)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+34, large)-Net in Base 27 — Upper bound on s

There is no (60, 94, large)-net in base 27, because

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