MinT - Best Known (75−42, 75, s)-Nets in Base 81

Best Known (75−42, 75, s)-Nets in Base 81

(75−42, 75, 370)-Net over F₈₁ — Constructive and digital

Digital (33, 75, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 75, 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]

(75−42, 75, 646)-Net over F₈₁ — Digital

Digital (33, 75, 646)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−42, 75, 710254)-Net in Base 81 — Upper bound on s

There is no (33, 75, 710255)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 136891 942399 235687 889059 452374 860233 838287 446829 110493 248867 616122 450438 318179 747606 317635 200366 016463 619065 038784 392614 490851 475292 251410 188401 > 81⁷⁵ [i]