MinT - Best Known (35, 35+45, s)-Nets in Base 81

Best Known (35, 35+45, s)-Nets in Base 81

(35, 35+45, 370)-Net over F₈₁ — Constructive and digital

Digital (35, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 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]

(35, 35+45, 659)-Net over F₈₁ — Digital

Digital (35, 80, 659)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 35+45, 807148)-Net in Base 81 — Upper bound on s

There is no (35, 80, 807149)-net in base 81, because

1 times m-reduction [i] would yield (35, 79, 807149)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5 892808 856522 270894 821008 368190 210056 655748 439794 896182 200837 256478 943326 485881 447747 997604 208801 446923 191653 541675 173399 378915 970466 106493 806111 302241 > 81⁷⁹ [i]