MinT - Best Known (66, 66+78, s)-Nets in Base 3

Best Known (66, 66+78, s)-Nets in Base 3

(66, 66+78, 48)-Net over F₃ — Constructive and digital

Digital (66, 144, 48)-net over F₃, using

t-expansion [i] based on digital (45, 144, 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]

(66, 66+78, 64)-Net over F₃ — Digital

Digital (66, 144, 64)-net over F₃, using

t-expansion [i] based on digital (49, 144, 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]

(66, 66+78, 407)-Net in Base 3 — Upper bound on s

There is no (66, 144, 408)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 528 707086 900142 320047 409540 816679 581812 844654 985694 363586 551072 778785 > 3¹⁴⁴ [i]