MinT - Best Known (14, 14+57, s)-Nets in Base 27

Best Known (14, 14+57, s)-Nets in Base 27

(14, 14+57, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 71, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 71, 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+57, 136)-Net over F₂₇ — Digital

Digital (14, 71, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 71, 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+57, 1631)-Net in Base 27 — Upper bound on s

There is no (14, 71, 1632)-net in base 27, because

1 times m-reduction [i] would yield (14, 70, 1632)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 15819 615969 375202 053604 537002 073576 716077 989874 255563 457357 079050 444983 264990 019459 564673 808259 688705 > 27⁷⁰ [i]