MinT - Best Known (54−30, 54, s)-Nets in Base 81

Best Known (54−30, 54, s)-Nets in Base 81

(54−30, 54, 370)-Net over F₈₁ — Constructive and digital

Digital (24, 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]

(54−30, 54, 537)-Net over F₈₁ — Digital

Digital (24, 54, 537)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−30, 54, 595960)-Net in Base 81 — Upper bound on s

There is no (24, 54, 595961)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 433951 940235 816650 520691 111631 080031 453899 807072 506346 429084 633414 245037 544534 721878 840852 916377 265201 > 81⁵⁴ [i]