MinT - Best Known (23, 23+37, s)-Nets in Base 81

Best Known (23, 23+37, s)-Nets in Base 81

(23, 23+37, 370)-Net over F₈₁ — Constructive and digital

Digital (23, 60, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 60, 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, 23+37, 170062)-Net in Base 81 — Upper bound on s

There is no (23, 60, 170063)-net in base 81, because

1 times m-reduction [i] would yield (23, 59, 170063)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39870 973696 963724 759306 942573 066007 455154 026543 131372 428266 039575 453158 007834 391424 787184 172870 406761 541248 717921 > 81⁵⁹ [i]