MinT - Best Known (15, 15+51, s)-Nets in Base 81

Best Known (15, 15+51, s)-Nets in Base 81

(15, 15+51, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 66, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 66, 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+51, 298)-Net over F₈₁ — Digital

Digital (15, 66, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 66, 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+51, 11644)-Net in Base 81 — Upper bound on s

There is no (15, 66, 11645)-net in base 81, because

1 times m-reduction [i] would yield (15, 65, 11645)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11260 627355 432521 304607 590285 724906 045239 777318 515996 472280 633908 812154 839080 556405 777390 571609 555959 219442 064487 181146 490001 > 81⁶⁵ [i]