MinT - Best Known (79−65, 79, s)-Nets in Base 81

Best Known (79−65, 79, s)-Nets in Base 81

(79−65, 79, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 79, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 79, 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]

(79−65, 79, 298)-Net over F₈₁ — Digital

Digital (14, 79, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 79, 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]

(79−65, 79, 7157)-Net in Base 81 — Upper bound on s

There is no (14, 79, 7158)-net in base 81, because

1 times m-reduction [i] would yield (14, 78, 7158)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 72923 050518 658296 811114 548469 651706 556470 779272 548084 513568 374916 483705 701917 298688 929153 511483 225295 394337 693796 129252 722571 287698 212989 342112 762881 > 81⁷⁸ [i]