MinT - Best Known (16, 16+52, s)-Nets in Base 81

Best Known (16, 16+52, s)-Nets in Base 81

(16, 16+52, 370)-Net over F₈₁ — Constructive and digital

Digital (16, 68, 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]

(16, 16+52, 12917)-Net in Base 81 — Upper bound on s

There is no (16, 68, 12918)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5984 123491 776114 464092 813655 676729 459582 026794 067693 971949 796580 243722 686339 513567 169386 820843 850672 807135 846654 933971 508518 549441 > 81⁶⁸ [i]