MinT - Best Known (65, 65+80, s)-Nets in Base 3

Best Known (65, 65+80, s)-Nets in Base 3

(65, 65+80, 48)-Net over F₃ — Constructive and digital

Digital (65, 145, 48)-net over F₃, using

t-expansion [i] based on digital (45, 145, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(65, 65+80, 64)-Net over F₃ — Digital

Digital (65, 145, 64)-net over F₃, using

t-expansion [i] based on digital (49, 145, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(65, 65+80, 384)-Net in Base 3 — Upper bound on s

There is no (65, 145, 385)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1529 787743 572293 987752 866682 535308 526708 280099 029839 124854 270628 710433 > 3¹⁴⁵ [i]