MinT - Best Known (77−66, 77, s)-Nets in Base 27

Best Known (77−66, 77, s)-Nets in Base 27

(77−66, 77, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 77, 96)-net over F₂₇, using

net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
  - an explicitly constructive algebraic function field [i]

(77−66, 77, 100)-Net over F₂₇ — Digital

Digital (11, 77, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(77−66, 77, 1089)-Net in Base 27 — Upper bound on s

There is no (11, 77, 1090)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 164 065546 477917 058273 161024 686103 308879 366140 876540 846794 215353 763718 629563 535814 208777 770109 280144 143618 253685 > 27⁷⁷ [i]