MinT - Best Known (14, 14+53, s)-Nets in Base 81

Best Known (14, 14+53, s)-Nets in Base 81

(14, 14+53, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 67, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 67, 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+53, 298)-Net over F₈₁ — Digital

Digital (14, 67, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 67, 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+53, 9209)-Net in Base 81 — Upper bound on s

There is no (14, 67, 9210)-net in base 81, because

1 times m-reduction [i] would yield (14, 66, 9210)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 914491 192478 178277 728578 065736 623195 977879 015204 020975 135365 458425 185150 015820 485965 941870 727678 112638 263175 407266 167653 556801 > 81⁶⁶ [i]