MinT - Best Known (82−60, 82, s)-Nets in Base 81

Best Known (82−60, 82, s)-Nets in Base 81

(82−60, 82, 370)-Net over F₈₁ — Constructive and digital

Digital (22, 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]

(82−60, 82, 24772)-Net in Base 81 — Upper bound on s

There is no (22, 82, 24773)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 134855 642291 335808 834368 503714 632207 299100 729619 168269 244155 568700 301430 669060 981851 024078 185189 176694 269448 169226 402164 003669 910975 049830 328896 451071 839201 > 81⁸² [i]