MinT - Best Known (18, 18+65, s)-Nets in Base 27

Best Known (18, 18+65, s)-Nets in Base 27

(18, 18+65, 108)-Net over F₂₇ — Constructive and digital

Digital (18, 83, 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+65, 148)-Net over F₂₇ — Digital

Digital (18, 83, 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+65, 2272)-Net in Base 27 — Upper bound on s

There is no (18, 83, 2273)-net in base 27, because

1 times m-reduction [i] would yield (18, 82, 2273)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2354 569838 882087 948551 825877 896771 231274 253105 538997 659672 608288 496647 164074 226299 081516 505399 926455 125531 054365 723521 > 27⁸² [i]