MinT - Best Known (250−48, 250, s)-Nets in Base 3

Best Known (250−48, 250, s)-Nets in Base 3

(250−48, 250, 896)-Net over F₃ — Constructive and digital

Digital (202, 250, 896)-net over F₃, using

3² 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]

(250−48, 250, 3192)-Net over F₃ — Digital

Digital (202, 250, 3192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−48, 250, 457428)-Net in Base 3 — Upper bound on s

There is no (202, 250, 457429)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190685 795673 295913 140518 608206 519406 849343 443847 894122 434687 368596 340090 786076 939951 382819 081671 135890 275774 423669 088033 > 3²⁵⁰ [i]