MinT - Best Known (31−20, 31, s)-Nets in Base 27

Best Known (31−20, 31, s)-Nets in Base 27

(31−20, 31, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 31, 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]

(31−20, 31, 100)-Net over F₂₇ — Digital

Digital (11, 31, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(31−20, 31, 116)-Net in Base 27 — Constructive

(11, 31, 116)-net in base 27, using

5 times m-reduction [i] based on (11, 36, 116)-net in base 27, using
- base change [i] based on digital (2, 27, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(31−20, 31, 136)-Net in Base 27

(11, 31, 136)-net in base 27, using

1 times m-reduction [i] based on (11, 32, 136)-net in base 27, using
- base change [i] based on digital (3, 24, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(31−20, 31, 4761)-Net in Base 27 — Upper bound on s

There is no (11, 31, 4762)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 235 676192 213117 612376 379824 851840 522809 291893 > 27³¹ [i]