MinT - Best Known (27−16, 27, s)-Nets in Base 27

Best Known (27−16, 27, s)-Nets in Base 27

(27−16, 27, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 27, 96)-net over F₂₇, using

net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
  - an explicitly constructive algebraic function field [i]

(27−16, 27, 101)-Net over F₂₇ — Digital

Digital (11, 27, 101)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(27−16, 27, 150)-Net in Base 27 — Constructive

(11, 27, 150)-net in base 27, using

1 times m-reduction [i] based on (11, 28, 150)-net in base 27, using
- base change [i] based on digital (4, 21, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(27−16, 27, 154)-Net in Base 27

(11, 27, 154)-net in base 27, using

1 times m-reduction [i] based on (11, 28, 154)-net in base 27, using
- base change [i] based on digital (4, 21, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

(27−16, 27, 9803)-Net in Base 27 — Upper bound on s

There is no (11, 27, 9804)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 443 446936 908923 763789 506629 004376 728001 > 27²⁷ [i]