MinT - Best Known (66−47, 66, s)-Nets in Base 81

Best Known (66−47, 66, s)-Nets in Base 81

(66−47, 66, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 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]

(66−47, 66, 29156)-Net in Base 81 — Upper bound on s

There is no (19, 66, 29157)-net in base 81, because

1 times m-reduction [i] would yield (19, 65, 29157)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11259 689446 739487 865743 047593 073550 910277 236585 426423 063437 792248 160545 790604 511065 050421 107536 274260 664215 862065 981842 954481 > 81⁶⁵ [i]