MinT - Best Known (54−37, 54, s)-Nets in Base 81

Best Known (54−37, 54, s)-Nets in Base 81

(54−37, 54, 370)-Net over F₈₁ — Constructive and digital

Digital (17, 54, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 54, 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]

(54−37, 54, 39298)-Net in Base 81 — Upper bound on s

There is no (17, 54, 39299)-net in base 81, because

1 times m-reduction [i] would yield (17, 53, 39299)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 141215 065002 701389 367045 780298 589541 758893 495783 843745 283843 494940 160911 766822 896539 395339 554965 710561 > 81⁵³ [i]