MinT - Best Known (20, 52, s)-Nets in Base 81

Best Known (20, 52, s)-Nets in Base 81

(20, 52, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 52, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 52, 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, 52, 135519)-Net in Base 81 — Upper bound on s

There is no (20, 52, 135520)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1742 887211 387212 245846 691461 838781 634785 055344 454012 415977 588384 337248 489395 839636 398703 414261 145601 > 81⁵² [i]