MinT - Best Known (212−52, 212, s)-Nets in Base 3

Best Known (212−52, 212, s)-Nets in Base 3

(212−52, 212, 400)-Net over F₃ — Constructive and digital

Digital (160, 212, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 53, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(212−52, 212, 961)-Net over F₃ — Digital

Digital (160, 212, 961)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−52, 212, 40960)-Net in Base 3 — Upper bound on s

There is no (160, 212, 40961)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141195 453179 093674 895059 164821 663860 425087 011273 016200 724737 578489 519666 713443 374289 619048 481781 104617 > 3²¹² [i]