MinT - Best Known (14, 14+32, s)-Nets in Base 81

Best Known (14, 14+32, s)-Nets in Base 81

(14, 14+32, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 46, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 46, 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]

(14, 14+32, 298)-Net over F₈₁ — Digital

Digital (14, 46, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 46, 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]

(14, 14+32, 26074)-Net in Base 81 — Upper bound on s

There is no (14, 46, 26075)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 6172 495944 742677 710001 138963 813155 539188 399959 731921 474970 360410 938435 660492 738990 176001 > 81⁴⁶ [i]