MinT - Best Known (48−32, 48, s)-Nets in Base 81

Best Known (48−32, 48, s)-Nets in Base 81

(48−32, 48, 370)-Net over F₈₁ — Constructive and digital

Digital (16, 48, 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]

(48−32, 48, 45167)-Net in Base 81 — Upper bound on s

There is no (16, 48, 45168)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 40 485397 527323 523023 323412 264690 034501 691351 622742 947166 390212 115343 791517 708870 723766 743041 > 81⁴⁸ [i]