MinT - Best Known (18, 59, s)-Nets in Base 81

Best Known (18, 59, s)-Nets in Base 81

(18, 59, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 59, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 59, 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, 59, 35538)-Net in Base 81 — Upper bound on s

There is no (18, 59, 35539)-net in base 81, because

1 times m-reduction [i] would yield (18, 58, 35539)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 492 222743 920690 034721 555543 897292 503090 763279 771322 221377 296313 912631 675305 274778 339194 499047 013553 210051 742401 > 81⁵⁸ [i]