MinT - Best Known (19, 19+39, s)-Nets in Base 81

Best Known (19, 19+39, s)-Nets in Base 81

(19, 19+39, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 58, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 58, 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+39, 52662)-Net in Base 81 — Upper bound on s

There is no (19, 58, 52663)-net in base 81, because

1 times m-reduction [i] would yield (19, 57, 52663)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 6 076712 113545 276126 364894 029864 165024 296260 638931 240897 161741 672013 954204 550943 628446 189636 652911 781938 838161 > 81⁵⁷ [i]