MinT - Best Known (59−33, 59, s)-Nets in Base 81

Best Known (59−33, 59, s)-Nets in Base 81

(59−33, 59, 370)-Net over F₈₁ — Constructive and digital

Digital (26, 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]

(59−33, 59, 544)-Net over F₈₁ — Digital

Digital (26, 59, 544)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−33, 59, 704209)-Net in Base 81 — Upper bound on s

There is no (26, 59, 704210)-net in base 81, because

1 times m-reduction [i] would yield (26, 58, 704210)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 492 188183 241262 950941 385321 784286 301075 550759 058111 799692 454815 275749 806652 217771 493183 402650 123458 197807 628801 > 81⁵⁸ [i]