MinT - Best Known (48, 48+82, s)-Nets in Base 3

Best Known (48, 48+82, s)-Nets in Base 3

(48, 48+82, 48)-Net over F₃ — Constructive and digital

Digital (48, 130, 48)-net over F₃, using

t-expansion [i] based on digital (45, 130, 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+82, 56)-Net over F₃ — Digital

Digital (48, 130, 56)-net over F₃, using

t-expansion [i] based on digital (40, 130, 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+82, 224)-Net in Base 3 — Upper bound on s

There is no (48, 130, 225)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 110 306407 893240 448308 598177 646858 616132 429561 633944 982285 512739 > 3¹³⁰ [i]