MinT - Best Known (14, 59, s)-Nets in Base 27

Best Known (14, 59, s)-Nets in Base 27

(14, 59, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 59, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 59, 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, 59, 136)-Net over F₂₇ — Digital

Digital (14, 59, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 59, 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, 59, 2056)-Net in Base 27 — Upper bound on s

There is no (14, 59, 2057)-net in base 27, because

1 times m-reduction [i] would yield (14, 58, 2057)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 105267 058762 224291 384631 126267 750035 232544 612854 833819 955386 155758 389746 053410 872409 > 27⁵⁸ [i]