MinT - Best Known (82−53, 82, s)-Nets in Base 81

Best Known (82−53, 82, s)-Nets in Base 81

(82−53, 82, 370)-Net over F₈₁ — Constructive and digital

Digital (29, 82, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 82, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(82−53, 82, 500)-Net over F₈₁ — Digital

Digital (29, 82, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 82, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(82−53, 82, 116364)-Net in Base 81 — Upper bound on s

There is no (29, 82, 116365)-net in base 81, because

1 times m-reduction [i] would yield (29, 81, 116365)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 38667 558670 919971 924577 332960 894866 954488 217527 594581 657497 304314 379472 894000 851163 654979 188712 067240 965533 188794 730098 627551 995300 227878 864473 114983 639201 > 81⁸¹ [i]