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

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

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

Digital (48, 96, 48)-net over F₃, using

t-expansion [i] based on digital (45, 96, 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+48, 56)-Net over F₃ — Digital

Digital (48, 96, 56)-net over F₃, using

t-expansion [i] based on digital (40, 96, 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+48, 374)-Net in Base 3 — Upper bound on s

There is no (48, 96, 375)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6723 233141 244158 740994 001618 324302 932936 715601 > 3⁹⁶ [i]