MinT - Best Known (65−43, 65, s)-Nets in Base 81

Best Known (65−43, 65, s)-Nets in Base 81

(65−43, 65, 370)-Net over F₈₁ — Constructive and digital

Digital (22, 65, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 65, 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]

(65−43, 65, 71068)-Net in Base 81 — Upper bound on s

There is no (22, 65, 71069)-net in base 81, because

1 times m-reduction [i] would yield (22, 64, 71069)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 139 042302 498842 579282 853356 344064 324581 779481 032257 060139 347465 864261 205348 635695 733285 016355 445074 813472 382861 478750 755921 > 81⁶⁴ [i]