MinT - Best Known (14, 14+61, s)-Nets in Base 27

Best Known (14, 14+61, s)-Nets in Base 27

(14, 14+61, 96)-Net over F₂₇ — Constructive and digital

Digital (14, 75, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 75, 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+61, 136)-Net over F₂₇ — Digital

Digital (14, 75, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 75, 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+61, 1556)-Net in Base 27 — Upper bound on s

There is no (14, 75, 1557)-net in base 27, because

1 times m-reduction [i] would yield (14, 74, 1557)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 8399 362457 869405 401743 517133 978781 322480 885311 591465 070840 399194 412381 339987 253259 321415 107819 000161 197297 > 27⁷⁴ [i]