MinT - Best Known (37−23, 37, s)-Nets in Base 27

Best Known (37−23, 37, s)-Nets in Base 27

(37−23, 37, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 37, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 37, 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]

(37−23, 37, 136)-Net over F₂₇ — Digital

Digital (14, 37, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 37, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(37−23, 37, 150)-Net in Base 27 — Constructive

(14, 37, 150)-net in base 27, using

3 times m-reduction [i] based on (14, 40, 150)-net in base 27, using
- base change [i] based on digital (4, 30, 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]

(37−23, 37, 154)-Net in Base 27

(14, 37, 154)-net in base 27, using

3 times m-reduction [i] based on (14, 40, 154)-net in base 27, using
- base change [i] based on digital (4, 30, 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]

(37−23, 37, 9125)-Net in Base 27 — Upper bound on s

There is no (14, 37, 9126)-net in base 27, because

1 times m-reduction [i] would yield (14, 36, 9126)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3384 338636 900572 153682 073186 639682 987275 499453 248673 > 27³⁶ [i]