MinT - Best Known (75−40, 75, s)-Nets in Base 81

Best Known (75−40, 75, s)-Nets in Base 81

(75−40, 75, 370)-Net over F₈₁ — Constructive and digital

Digital (35, 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]

(75−40, 75, 920)-Net over F₈₁ — Digital

Digital (35, 75, 920)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−40, 75, 1489471)-Net in Base 81 — Upper bound on s

There is no (35, 75, 1489472)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 136892 246290 098325 235348 219135 748027 208799 034523 949157 384845 584070 790562 282723 421242 175598 139039 115496 492786 540051 483171 974585 460370 903971 123201 > 81⁷⁵ [i]