MinT - Best Known (3, 14, s)-Nets in Base 81

Best Known (3, 14, s)-Nets in Base 81

(3, 14, 116)-Net over F₈₁ — Constructive and digital

Digital (3, 14, 116)-net over F₈₁, using

t-expansion [i] based on digital (2, 14, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(3, 14, 136)-Net over F₈₁ — Digital

Digital (3, 14, 136)-net over F₈₁, using

net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
  - a curve from the manYPoints database [i]

(3, 14, 2981)-Net in Base 81 — Upper bound on s

There is no (3, 14, 2982)-net in base 81, because

1 times m-reduction [i] would yield (3, 13, 2982)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 6 461122 710608 387378 664801 > 81¹³ [i]