MinT - Best Known (212−94, 212, s)-Nets in Base 3

Best Known (212−94, 212, s)-Nets in Base 3

(212−94, 212, 84)-Net over F₃ — Constructive and digital

Digital (118, 212, 84)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 73, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
      - an explicitly constructive algebraic function field [i]
2. digital (45, 139, 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]

(212−94, 212, 147)-Net over F₃ — Digital

Digital (118, 212, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−94, 212, 1257)-Net in Base 3 — Upper bound on s

There is no (118, 212, 1258)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141577 327884 291186 652620 166953 532134 460941 672020 276213 258691 338013 003824 117416 064568 267863 477544 714297 > 3²¹² [i]