MinT - Best Known (18, 18+58, s)-Nets in Base 27

Best Known (18, 18+58, s)-Nets in Base 27

(18, 18+58, 108)-Net over F₂₇ — Constructive and digital

Digital (18, 76, 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+58, 148)-Net over F₂₇ — Digital

Digital (18, 76, 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+58, 2516)-Net in Base 27 — Upper bound on s

There is no (18, 76, 2517)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 146233 447407 318293 223630 750734 608566 589549 894102 948592 955440 851323 316115 682511 074635 884974 464856 865198 338291 > 27⁷⁶ [i]