MinT - Best Known (15, 15+41, s)-Nets in Base 81

Best Known (15, 15+41, s)-Nets in Base 81

(15, 15+41, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 56, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 56, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(15, 15+41, 298)-Net over F₈₁ — Digital

Digital (15, 56, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 56, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(15, 15+41, 18378)-Net in Base 81 — Upper bound on s

There is no (15, 56, 18379)-net in base 81, because

1 times m-reduction [i] would yield (15, 55, 18379)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 926 229915 900554 233867 283581 297446 392769 988764 978672 888163 441914 892022 128237 673495 210962 075296 968758 366401 > 81⁵⁵ [i]