MinT - Best Known (51, 51+74, s)-Nets in Base 3

Best Known (51, 51+74, s)-Nets in Base 3

(51, 51+74, 48)-Net over F₃ — Constructive and digital

Digital (51, 125, 48)-net over F₃, using

t-expansion [i] based on digital (45, 125, 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]

(51, 51+74, 64)-Net over F₃ — Digital

Digital (51, 125, 64)-net over F₃, using

t-expansion [i] based on digital (49, 125, 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]

(51, 51+74, 265)-Net in Base 3 — Upper bound on s

There is no (51, 125, 266)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 494071 375875 879376 109059 354158 174603 880265 116945 810489 158189 > 3¹²⁵ [i]