MinT - Best Known (22, 22+58, s)-Nets in Base 81

Best Known (22, 22+58, s)-Nets in Base 81

(22, 22+58, 370)-Net over F₈₁ — Constructive and digital

Digital (22, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 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]

(22, 22+58, 26827)-Net in Base 81 — Upper bound on s

There is no (22, 80, 26828)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 477 387977 175905 682475 343850 936327 714436 466259 868526 243541 613021 608004 456794 938227 686164 222725 849235 699565 341798 173234 075912 446113 093588 442188 019357 191361 > 81⁸⁰ [i]