MinT - Best Known (15, 15+63, s)-Nets in Base 81

Best Known (15, 15+63, s)-Nets in Base 81

(15, 15+63, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 78, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 78, 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+63, 298)-Net over F₈₁ — Digital

Digital (15, 78, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 78, 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+63, 8522)-Net in Base 81 — Upper bound on s

There is no (15, 78, 8523)-net in base 81, because

1 times m-reduction [i] would yield (15, 77, 8523)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 898 278561 702880 577102 171637 566612 947973 330231 466992 137368 127276 199811 731021 037628 662481 826888 683986 193092 682273 012528 094226 351923 049098 484994 513041 > 81⁷⁷ [i]