MinT - Best Known (68−50, 68, s)-Nets in Base 81

Best Known (68−50, 68, s)-Nets in Base 81

(68−50, 68, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 68, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 68, 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]

(68−50, 68, 19739)-Net in Base 81 — Upper bound on s

There is no (18, 68, 19740)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5984 830635 762934 957310 576057 500385 376877 416828 327981 525005 558148 755205 929594 517735 191967 853336 395666 226614 531335 297101 360045 880001 > 81⁶⁸ [i]