MinT - Best Known (19, 19+41, s)-Nets in Base 81

Best Known (19, 19+41, s)-Nets in Base 81

(19, 19+41, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 60, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 60, 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+41, 44274)-Net in Base 81 — Upper bound on s

There is no (19, 60, 44275)-net in base 81, because

1 times m-reduction [i] would yield (19, 59, 44275)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39880 352171 277255 029871 860357 298032 690815 867547 190083 578883 603321 083443 215750 550513 068372 586688 197469 294090 040001 > 81⁵⁹ [i]