MinT - Best Known (18, 18+30, s)-Nets in Base 81

Best Known (18, 18+30, s)-Nets in Base 81

(18, 18+30, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 48, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 48, 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+30, 102753)-Net in Base 81 — Upper bound on s

There is no (18, 48, 102754)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 40 484324 904878 353758 034710 357240 194032 154354 230019 068693 107946 596673 415897 741226 108831 624801 > 81⁴⁸ [i]