MinT - Best Known (59−31, 59, s)-Nets in Base 81

Best Known (59−31, 59, s)-Nets in Base 81

(59−31, 59, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 59, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 59, 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]

(59−31, 59, 868)-Net over F₈₁ — Digital

Digital (28, 59, 868)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−31, 59, 1923757)-Net in Base 81 — Upper bound on s

There is no (28, 59, 1923758)-net in base 81, because

1 times m-reduction [i] would yield (28, 58, 1923758)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 492 188107 372893 178458 568581 275039 475504 878400 832437 574959 181932 802206 791677 966039 551763 125055 978914 138576 701601 > 81⁵⁸ [i]