MinT - Best Known (249−58, 249, s)-Nets in Base 3

Best Known (249−58, 249, s)-Nets in Base 3

(249−58, 249, 600)-Net over F₃ — Constructive and digital

Digital (191, 249, 600)-net over F₃, using

3¹ times duplication [i] based on digital (190, 248, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 62, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(249−58, 249, 1358)-Net over F₃ — Digital

Digital (191, 249, 1358)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−58, 249, 72875)-Net in Base 3 — Upper bound on s

There is no (191, 249, 72876)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63563 234348 567324 395462 630664 511566 281944 261717 789071 755254 019386 634047 225668 536326 213859 933832 969304 071019 129801 696313 > 3²⁴⁹ [i]