MinT - Best Known (23, 66, s)-Nets in Base 81

Best Known (23, 66, s)-Nets in Base 81

(23, 66, 370)-Net over F₈₁ — Constructive and digital

Digital (23, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(23, 66, 87612)-Net in Base 81 — Upper bound on s

There is no (23, 66, 87613)-net in base 81, because

1 times m-reduction [i] would yield (23, 65, 87613)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11260 394254 327702 119350 466605 560719 217200 720329 295263 393127 316613 975258 371398 422097 855012 753825 936178 508678 912419 534234 293841 > 81⁶⁵ [i]