MinT - Best Known (6, 6+17, s)-Nets in Base 27

Best Known (6, 6+17, s)-Nets in Base 27

(6, 6+17, 76)-Net over F₂₇ — Constructive and digital

Digital (6, 23, 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]

(6, 6+17, 82)-Net in Base 27 — Constructive

(6, 23, 82)-net in base 27, using

1 times m-reduction [i] based on (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]

(6, 6+17, 1246)-Net in Base 27 — Upper bound on s

There is no (6, 23, 1247)-net in base 27, because

1 times m-reduction [i] would yield (6, 22, 1247)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 31 030037 407461 668716 807017 241905 > 27²² [i]