MinT - Best Known (21, 54, s)-Nets in Base 81

Best Known (21, 54, s)-Nets in Base 81

(21, 54, 370)-Net over F₈₁ — Constructive and digital

Digital (21, 54, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 54, 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]

(21, 54, 178355)-Net in Base 81 — Upper bound on s

There is no (21, 54, 178356)-net in base 81, because

1 times m-reduction [i] would yield (21, 53, 178356)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 141163 936552 943550 151429 324353 312325 861663 827749 672728 139741 209784 745914 442186 253625 222927 380799 943681 > 81⁵³ [i]