MinT - Best Known (18, 18+37, s)-Nets in Base 81

Best Known (18, 18+37, s)-Nets in Base 81

(18, 18+37, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 55, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 55, 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+37, 50167)-Net in Base 81 — Upper bound on s

There is no (18, 55, 50168)-net in base 81, because

1 times m-reduction [i] would yield (18, 54, 50168)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 437215 660951 615143 060948 163551 468666 593099 770760 730299 120101 987687 851173 723693 527490 728376 721891 045121 > 81⁵⁴ [i]