MinT - Best Known (249−48, 249, s)-Nets in Base 3

Best Known (249−48, 249, s)-Nets in Base 3

(249−48, 249, 896)-Net over F₃ — Constructive and digital

Digital (201, 249, 896)-net over F₃, using

3¹ times duplication [i] based on digital (200, 248, 896)-net over F₃, using
- t-expansion [i] based on digital (199, 248, 896)-net over F₃, using
  - trace code for nets [i] based on digital (13, 62, 224)-net over F₈₁, using
    - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
        a function field by SÃ©mirat [i]

(249−48, 249, 3119)-Net over F₃ — Digital

Digital (201, 249, 3119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−48, 249, 436960)-Net in Base 3 — Upper bound on s

There is no (201, 249, 436961)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63562 211196 464979 300557 612009 118102 461457 323932 332381 751087 581764 660727 753333 077598 516164 816607 569180 363196 483321 575649 > 3²⁴⁹ [i]