MinT - Best Known (14, 89, s)-Nets in Base 27

Best Known (14, 89, s)-Nets in Base 27

(14, 89, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 89, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 89, 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]

(14, 89, 136)-Net over F₂₇ — Digital

Digital (14, 89, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 89, 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]

(14, 89, 1410)-Net in Base 27 — Upper bound on s

There is no (14, 89, 1411)-net in base 27, because

1 times m-reduction [i] would yield (14, 88, 1411)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 926422 342331 087538 523559 955484 102031 127147 077815 758482 452133 396712 280406 082032 456946 295528 314495 888954 184045 651722 301325 724711 > 27⁸⁸ [i]