MinT - Best Known (48, 48+64, s)-Nets in Base 3

Best Known (48, 48+64, s)-Nets in Base 3

(48, 48+64, 48)-Net over F₃ — Constructive and digital

Digital (48, 112, 48)-net over F₃, using

t-expansion [i] based on digital (45, 112, 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]

(48, 48+64, 56)-Net over F₃ — Digital

Digital (48, 112, 56)-net over F₃, using

t-expansion [i] based on digital (40, 112, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(48, 48+64, 268)-Net in Base 3 — Upper bound on s

There is no (48, 112, 269)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 277383 407252 928023 257694 750531 210585 334057 326161 202049 > 3¹¹² [i]