MinT - Best Known (19, 19+31, s)-Nets in Base 81

Best Known (19, 19+31, s)-Nets in Base 81

(19, 19+31, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 50, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 50, 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+31, 137733)-Net in Base 81 — Upper bound on s

There is no (19, 50, 137734)-net in base 81, because

1 times m-reduction [i] would yield (19, 49, 137734)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3279 499223 727633 919825 626158 019408 980713 295208 687527 328204 619456 993023 034638 654065 357565 120801 > 81⁴⁹ [i]