MinT - Best Known (11, 60, s)-Nets in Base 27

Best Known (11, 60, s)-Nets in Base 27

(11, 60, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 60, 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]

(11, 60, 100)-Net over F₂₇ — Digital

Digital (11, 60, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(11, 60, 1232)-Net in Base 27 — Upper bound on s

There is no (11, 60, 1233)-net in base 27, because

1 times m-reduction [i] would yield (11, 59, 1233)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2 844630 562689 338375 771659 355223 428370 568835 167327 407087 318803 976745 626851 104449 634977 > 27⁵⁹ [i]