MinT - Best Known (18, 18+34, s)-Nets in Base 81

Best Known (18, 18+34, s)-Nets in Base 81

(18, 18+34, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 52, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 52, 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]

(18, 18+34, 61732)-Net in Base 81 — Upper bound on s

There is no (18, 52, 61733)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1742 765109 261570 095383 911121 264132 547305 661259 056187 230945 729607 521562 649466 267571 896649 116893 531281 > 81⁵² [i]