MinT - Best Known (52, 52+54, s)-Nets in Base 3

Best Known (52, 52+54, s)-Nets in Base 3

(52, 52+54, 48)-Net over F₃ — Constructive and digital

Digital (52, 106, 48)-net over F₃, using

t-expansion [i] based on digital (45, 106, 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]

(52, 52+54, 64)-Net over F₃ — Digital

Digital (52, 106, 64)-net over F₃, using

t-expansion [i] based on digital (49, 106, 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]

(52, 52+54, 382)-Net in Base 3 — Upper bound on s

There is no (52, 106, 383)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 399 769649 931170 955303 865717 498475 044739 048713 926091 > 3¹⁰⁶ [i]