MinT - Best Known (52−35, 52, s)-Nets in Base 81

Best Known (52−35, 52, s)-Nets in Base 81

(52−35, 52, 370)-Net over F₈₁ — Constructive and digital

Digital (17, 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]

(52−35, 52, 47668)-Net in Base 81 — Upper bound on s

There is no (17, 52, 47669)-net in base 81, because

1 times m-reduction [i] would yield (17, 51, 47669)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 21 515218 983917 067749 031578 267719 405045 168794 375912 340894 286975 565149 321030 327042 392936 551614 525841 > 81⁵¹ [i]