MinT - Best Known (18, 69, s)-Nets in Base 27

Best Known (18, 69, s)-Nets in Base 27

(18, 69, 108)-Net over F₂₇ — Constructive and digital

Digital (18, 69, 108)-net over F₂₇, using

net from sequence [i] based on digital (18, 107)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 108, using
  - F₃ from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F₂₇ [i]

(18, 69, 148)-Net over F₂₇ — Digital

Digital (18, 69, 148)-net over F₂₇, using

net from sequence [i] based on digital (18, 147)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 18 and N(F) ≥ 148, using
  - a curve from the manYPoints database [i]

(18, 69, 3048)-Net in Base 27 — Upper bound on s

There is no (18, 69, 3049)-net in base 27, because

1 times m-reduction [i] would yield (18, 68, 3049)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 21 559433 848869 474896 044543 155595 562110 856165 305003 535313 076971 981906 860654 306820 119025 802823 264523 > 27⁶⁸ [i]