MinT - Best Known (24, 24+56, s)-Nets in Base 81

Best Known (24, 24+56, s)-Nets in Base 81

(24, 24+56, 370)-Net over F₈₁ — Constructive and digital

Digital (24, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 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]

(24, 24+56, 40047)-Net in Base 81 — Upper bound on s

There is no (24, 80, 40048)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 477 360571 616948 876583 815381 265776 612455 130523 804171 787648 604077 224204 224654 108769 974804 998401 014655 637276 644560 523626 713346 913289 042273 164826 614697 886721 > 81⁸⁰ [i]