MinT - Best Known (15, 40, s)-Nets in Base 27

Best Known (15, 40, s)-Nets in Base 27

(15, 40, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 40, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 40, 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]

(15, 40, 136)-Net over F₂₇ — Digital

Digital (15, 40, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 40, 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]

(15, 40, 160)-Net in Base 27 — Constructive

(15, 40, 160)-net in base 27, using

base change [i] based on digital (5, 30, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(15, 40, 167)-Net in Base 27

(15, 40, 167)-net in base 27, using

base change [i] based on digital (5, 30, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(15, 40, 9120)-Net in Base 27 — Upper bound on s

There is no (15, 40, 9121)-net in base 27, because

1 times m-reduction [i] would yield (15, 39, 9121)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 66 566744 607175 259164 367331 197166 659265 031269 289430 388689 > 27³⁹ [i]