MinT - Best Known (27, 27+50, s)-Nets in Base 81

Best Known (27, 27+50, s)-Nets in Base 81

(27, 27+50, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 77, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 77, 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]

(27, 27+50, 500)-Net over F₈₁ — Digital

Digital (27, 77, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 77, 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]

(27, 27+50, 96075)-Net in Base 81 — Upper bound on s

There is no (27, 77, 96076)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 898 189803 506921 582812 629017 796747 287044 900148 852453 920442 123502 010197 970144 242072 449558 045918 917535 275519 597545 742759 369098 756193 029564 646475 672001 > 81⁷⁷ [i]