MinT - Best Known (19, 19+37, s)-Nets in Base 81

Best Known (19, 19+37, s)-Nets in Base 81

(19, 19+37, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 56, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 56, 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]

(19, 19+37, 64041)-Net in Base 81 — Upper bound on s

There is no (19, 56, 64042)-net in base 81, because

1 times m-reduction [i] would yield (19, 55, 64042)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 926 214584 875084 810122 342376 567555 703759 767422 068452 548538 974664 241350 761390 679878 839173 198013 243295 286081 > 81⁵⁵ [i]