MinT - Best Known (12, 12+17, s)-Nets in Base 27

Best Known (12, 12+17, s)-Nets in Base 27

(12, 12+17, 96)-Net over F₂₇ — Constructive and digital

Digital (12, 29, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 29, 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]

(12, 12+17, 110)-Net over F₂₇ — Digital

Digital (12, 29, 110)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(12, 12+17, 150)-Net in Base 27 — Constructive

(12, 29, 150)-net in base 27, using

3 times m-reduction [i] based on (12, 32, 150)-net in base 27, using
- base change [i] based on digital (4, 24, 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]

(12, 12+17, 154)-Net in Base 27

(12, 29, 154)-net in base 27, using

3 times m-reduction [i] based on (12, 32, 154)-net in base 27, using
- base change [i] based on digital (4, 24, 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]

(12, 12+17, 14803)-Net in Base 27 — Upper bound on s

There is no (12, 29, 14804)-net in base 27, because

1 times m-reduction [i] would yield (12, 28, 14804)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11972 706219 265745 649288 107726 002667 096001 > 27²⁸ [i]