MinT - Best Known (22, 77, s)-Nets in Base 81

Best Known (22, 77, s)-Nets in Base 81

(22, 77, 370)-Net over F₈₁ — Constructive and digital

Digital (22, 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]

(22, 77, 32149)-Net in Base 81 — Upper bound on s

There is no (22, 77, 32150)-net in base 81, because

1 times m-reduction [i] would yield (22, 76, 32150)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 096764 724266 892496 133327 825947 113512 456727 857747 284314 942571 187340 469924 154270 684937 129318 675421 789160 822378 834069 954931 718014 488780 546572 324001 > 81⁷⁶ [i]