MinT - Best Known (32, 32+38, s)-Nets in Base 81

Best Known (32, 32+38, s)-Nets in Base 81

(32, 32+38, 370)-Net over F₈₁ — Constructive and digital

Digital (32, 70, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 70, 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]

(32, 32+38, 766)-Net over F₈₁ — Digital

Digital (32, 70, 766)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 32+38, 1065080)-Net in Base 81 — Upper bound on s

There is no (32, 70, 1065081)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39 260588 721292 607446 460622 045580 476663 109168 471501 827328 811918 293619 711794 047929 784329 522429 468003 041157 697199 727060 786751 405227 953521 > 81⁷⁰ [i]