MinT - Best Known (18, 18+53, s)-Nets in Base 27

Best Known (18, 18+53, s)-Nets in Base 27

(18, 18+53, 108)-Net over F₂₇ — Constructive and digital

Digital (18, 71, 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, 18+53, 148)-Net over F₂₇ — Digital

Digital (18, 71, 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, 18+53, 2883)-Net in Base 27 — Upper bound on s

There is no (18, 71, 2884)-net in base 27, because

1 times m-reduction [i] would yield (18, 70, 2884)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 15712 393479 569098 038460 602984 186180 541652 940514 885603 515272 919789 373150 645424 196046 776228 497792 133945 > 27⁷⁰ [i]