MinT - Best Known (138−78, 138, s)-Nets in Base 3

Best Known (138−78, 138, s)-Nets in Base 3

(138−78, 138, 48)-Net over F₃ — Constructive and digital

Digital (60, 138, 48)-net over F₃, using

t-expansion [i] based on digital (45, 138, 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]

(138−78, 138, 64)-Net over F₃ — Digital

Digital (60, 138, 64)-net over F₃, using

t-expansion [i] based on digital (49, 138, 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]

(138−78, 138, 338)-Net in Base 3 — Upper bound on s

There is no (60, 138, 339)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 724896 600768 838852 406551 849673 164228 810821 112950 667582 598821 380099 > 3¹³⁸ [i]