MinT - Best Known (246−120, 246, s)-Nets in Base 3

Best Known (246−120, 246, s)-Nets in Base 3

(246−120, 246, 80)-Net over F₃ — Constructive and digital

Digital (126, 246, 80)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (21, 81, 32)-net over F₃, using
  - net from sequence [i] based on digital (21, 31)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
      - an explicitly constructive algebraic function field [i]
2. digital (45, 165, 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]

(246−120, 246, 129)-Net over F₃ — Digital

Digital (126, 246, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−120, 246, 990)-Net in Base 3 — Upper bound on s

There is no (126, 246, 991)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2463 369884 653380 981661 650378 326178 096099 969565 881059 114730 090134 151652 965359 972786 088026 375919 913960 592467 178827 997577 > 3²⁴⁶ [i]