MinT - Best Known (18, 18+48, s)-Nets in Base 27

Best Known (18, 18+48, s)-Nets in Base 27

(18, 18+48, 108)-Net over F₂₇ — Constructive and digital

Digital (18, 66, 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+48, 148)-Net over F₂₇ — Digital

Digital (18, 66, 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+48, 3243)-Net in Base 27 — Upper bound on s

There is no (18, 66, 3244)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 29675 639929 085289 600439 914129 114458 212741 302416 159710 293736 342310 671279 785963 328399 932439 857729 > 27⁶⁶ [i]