MinT - Best Known (20, 20+57, s)-Nets in Base 81

Best Known (20, 20+57, s)-Nets in Base 81

(20, 20+57, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 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]

(20, 20+57, 21370)-Net in Base 81 — Upper bound on s

There is no (20, 77, 21371)-net in base 81, because

1 times m-reduction [i] would yield (20, 76, 21371)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 100732 872423 484836 648839 451006 636211 338442 272573 452979 392824 044205 458889 196671 439079 995129 978709 603947 074831 796889 260264 506450 444243 508546 738241 > 81⁷⁶ [i]