MinT - Best Known (19, 77, s)-Nets in Base 81

Best Known (19, 77, s)-Nets in Base 81

(19, 77, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 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]

(19, 77, 17022)-Net in Base 81 — Upper bound on s

There is no (19, 77, 17023)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 898 954299 230861 544580 298937 823281 437512 125316 488339 897656 499689 397712 566817 687971 349438 730795 884441 243622 833706 676791 049050 904773 452822 598471 851761 > 81⁷⁷ [i]