MinT - Best Known (15, 15+67, s)-Nets in Base 81

Best Known (15, 15+67, s)-Nets in Base 81

(15, 15+67, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 82, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 82, 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+67, 298)-Net over F₈₁ — Digital

Digital (15, 82, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 82, 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+67, 7940)-Net in Base 81 — Upper bound on s

There is no (15, 82, 7941)-net in base 81, because

1 times m-reduction [i] would yield (15, 81, 7941)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 38792 152832 146430 703841 747704 097016 155795 244092 939818 174184 322275 017308 373584 424498 986649 274889 866685 434554 134794 662754 029627 855325 226521 856156 592450 327441 > 81⁸¹ [i]