MinT - Best Known (14, 14+64, s)-Nets in Base 27

Best Known (14, 14+64, s)-Nets in Base 27

(14, 14+64, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 78, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 78, 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, 14+64, 136)-Net over F₂₇ — Digital

Digital (14, 78, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 78, 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, 14+64, 1499)-Net in Base 27 — Upper bound on s

There is no (14, 78, 1500)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4442 945059 573159 380743 948491 704891 184695 202192 493835 905027 899489 804928 857603 738957 389367 620077 683441 479200 712961 > 27⁷⁸ [i]