MinT - Best Known (81−54, 81, s)-Nets in Base 81

Best Known (81−54, 81, s)-Nets in Base 81

(81−54, 81, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 81, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 81, 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]

(81−54, 81, 500)-Net over F₈₁ — Digital

Digital (27, 81, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 81, 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]

(81−54, 81, 72559)-Net in Base 81 — Upper bound on s

There is no (27, 81, 72560)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 38674 826012 667483 929510 120999 655362 490606 199138 220244 061046 618419 289521 983197 505119 211780 397068 222795 262046 503054 096654 216706 837154 480946 353817 682659 641601 > 81⁸¹ [i]