MinT - Best Known (8, 8+18, s)-Nets in Base 27

Best Known (8, 8+18, s)-Nets in Base 27

(8, 8+18, 84)-Net over F₂₇ — Constructive and digital

Digital (8, 26, 84)-net over F₂₇, using

net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
  - a function field by SÃ©mirat [i]

(8, 8+18, 92)-Net over F₂₇ — Digital

Digital (8, 26, 92)-net over F₂₇, using

net from sequence [i] based on digital (8, 91)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 92, using
  - a curve from the manYPoints database [i]

(8, 8+18, 100)-Net in Base 27 — Constructive

(8, 26, 100)-net in base 27, using

2 times m-reduction [i] based on (8, 28, 100)-net in base 27, using
- base change [i] based on digital (1, 21, 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]

(8, 8+18, 2172)-Net in Base 27 — Upper bound on s

There is no (8, 26, 2173)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 16 456613 649904 937397 029680 377432 139859 > 27²⁶ [i]