MinT - Best Known (66−39, 66, s)-Nets in Base 81

Best Known (66−39, 66, s)-Nets in Base 81

(66−39, 66, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 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]

(66−39, 66, 500)-Net over F₈₁ — Digital

Digital (27, 66, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 66, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(66−39, 66, 335074)-Net in Base 81 — Upper bound on s

There is no (27, 66, 335075)-net in base 81, because

1 times m-reduction [i] would yield (27, 65, 335075)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11260 070507 294409 954446 473925 305658 508750 980813 535545 355440 513590 227727 898727 067208 381145 202384 484001 897921 251016 699087 554001 > 81⁶⁵ [i]