MinT - Best Known (19, 48, s)-Nets in Base 81

Best Known (19, 48, s)-Nets in Base 81

(19, 48, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 48, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 48, 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, 48, 192934)-Net in Base 81 — Upper bound on s

There is no (19, 48, 192935)-net in base 81, because

1 times m-reduction [i] would yield (19, 47, 192935)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 499822 827544 521112 182046 841307 232425 974206 825417 337089 879222 046560 012401 150773 443916 439201 > 81⁴⁷ [i]