MinT - Best Known (65−45, 65, s)-Nets in Base 81

Best Known (65−45, 65, s)-Nets in Base 81

(65−45, 65, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 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]

(65−45, 65, 40327)-Net in Base 81 — Upper bound on s

There is no (20, 65, 40328)-net in base 81, because

1 times m-reduction [i] would yield (20, 64, 40328)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 139 031275 544371 532061 764747 390520 139822 934350 626132 763391 039821 657708 106607 160974 201965 719467 824920 371474 691319 927647 527681 > 81⁶⁴ [i]