MinT - Best Known (43−29, 43, s)-Nets in Base 81

Best Known (43−29, 43, s)-Nets in Base 81

(43−29, 43, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 43, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 43, 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]

(43−29, 43, 298)-Net over F₈₁ — Digital

Digital (14, 43, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 43, 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]

(43−29, 43, 40156)-Net in Base 81 — Upper bound on s

There is no (14, 43, 40157)-net in base 81, because

1 times m-reduction [i] would yield (14, 42, 40157)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 143 390258 951964 696913 044437 826070 085170 525377 542416 474789 397746 107548 738315 395041 > 81⁴² [i]