MinT - Best Known (6, 18, s)-Nets in Base 27

Best Known (6, 18, s)-Nets in Base 27

(6, 18, 76)-Net over F₂₇ — Constructive and digital

Digital (6, 18, 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, 18, 100)-Net in Base 27 — Constructive

(6, 18, 100)-net in base 27, using

2 times m-reduction [i] based on (6, 20, 100)-net in base 27, using
- base change [i] based on digital (1, 15, 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]

(6, 18, 2263)-Net in Base 27 — Upper bound on s

There is no (6, 18, 2264)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 58 197749 054363 129746 340625 > 27¹⁸ [i]