MinT - Best Known (65−35, 65, s)-Nets in Base 81

Best Known (65−35, 65, s)-Nets in Base 81

(65−35, 65, 370)-Net over F₈₁ — Constructive and digital

Digital (30, 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]

(65−35, 65, 770)-Net over F₈₁ — Digital

Digital (30, 65, 770)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−35, 65, 1373211)-Net in Base 81 — Upper bound on s

There is no (30, 65, 1373212)-net in base 81, because

1 times m-reduction [i] would yield (30, 64, 1373212)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 139 009488 759199 129998 903003 685674 829047 662186 646371 165539 658913 025003 606396 029172 041911 165445 843308 062661 905103 536844 899521 > 81⁶⁴ [i]