MinT - Best Known (19, 19+56, s)-Nets in Base 81

Best Known (19, 19+56, s)-Nets in Base 81

(19, 19+56, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 75, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 75, 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]

(19, 19+56, 18264)-Net in Base 81 — Upper bound on s

There is no (19, 75, 18265)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 137071 063575 956977 276246 577697 125648 316124 171407 898284 075039 925824 383892 228201 896271 372229 139697 309610 247556 168398 519187 749472 017520 410914 577601 > 81⁷⁵ [i]