MinT - Best Known (15, 62, s)-Nets in Base 81

Best Known (15, 62, s)-Nets in Base 81

(15, 62, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 62, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 62, 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, 62, 298)-Net over F₈₁ — Digital

Digital (15, 62, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 62, 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, 62, 13571)-Net in Base 81 — Upper bound on s

There is no (15, 62, 13572)-net in base 81, because

1 times m-reduction [i] would yield (15, 61, 13572)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 261 629340 071825 327213 582640 577859 866278 409079 726250 483482 477649 380450 071995 435473 897185 309993 904043 212161 419403 878081 > 81⁶¹ [i]