MinT - Best Known (15, 80, s)-Nets in Base 81

Best Known (15, 80, s)-Nets in Base 81

(15, 80, 224)-Net over F₈₁ — Constructive and digital

Digital (15, 80, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 80, 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, 80, 298)-Net over F₈₁ — Digital

Digital (15, 80, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 80, 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, 80, 8213)-Net in Base 81 — Upper bound on s

There is no (15, 80, 8214)-net in base 81, because

1 times m-reduction [i] would yield (15, 79, 8214)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5 906411 037388 410331 663536 997570 515717 150202 872832 198485 151499 785749 833455 364894 669744 764505 179843 722040 563559 775982 981204 479680 091430 995340 252504 099841 > 81⁷⁹ [i]