MinT - Best Known (21, 21+25, s)-Nets in Base 81

Best Known (21, 21+25, s)-Nets in Base 81

(21, 21+25, 370)-Net over F₈₁ — Constructive and digital

Digital (21, 46, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 46, 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]

(21, 21+25, 569)-Net over F₈₁ — Digital

Digital (21, 46, 569)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(21, 21+25, 948609)-Net in Base 81 — Upper bound on s

There is no (21, 46, 948610)-net in base 81, because

1 times m-reduction [i] would yield (21, 45, 948610)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 76 177427 537981 309969 926699 879398 461646 923509 610785 194535 796865 951117 250414 452516 617601 > 81⁴⁵ [i]