MinT - Best Known (15, 15+34, s)-Nets in Base 81

Best Known (15, 15+34, s)-Nets in Base 81

(15, 15+34, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 49, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 49, 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+34, 298)-Net over F₈₁ — Digital

Digital (15, 49, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 49, 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+34, 28422)-Net in Base 81 — Upper bound on s

There is no (15, 49, 28423)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3280 821643 834872 777695 556257 833222 267593 753425 453856 102087 446102 075352 008840 876487 849535 845681 > 81⁴⁹ [i]