MinT - Best Known (27, 27+31, s)-Nets in Base 81

Best Known (27, 27+31, s)-Nets in Base 81

(27, 27+31, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 58, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 58, 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]

(27, 27+31, 752)-Net over F₈₁ — Digital

Digital (27, 58, 752)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 27+31, 1435216)-Net in Base 81 — Upper bound on s

There is no (27, 58, 1435217)-net in base 81, because

1 times m-reduction [i] would yield (27, 57, 1435217)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 6 076400 154515 818696 182385 165079 747719 307940 675688 374415 589725 195058 083627 344913 453759 970966 006931 961860 916401 > 81⁵⁷ [i]