MinT - Best Known (250−70, 250, s)-Nets in Base 3

Best Known (250−70, 250, s)-Nets in Base 3

(250−70, 250, 288)-Net over F₃ — Constructive and digital

Digital (180, 250, 288)-net over F₃, using

3¹ times duplication [i] based on digital (179, 249, 288)-net over F₃, using
- t-expansion [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(250−70, 250, 676)-Net over F₃ — Digital

Digital (180, 250, 676)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−70, 250, 17758)-Net in Base 3 — Upper bound on s

There is no (180, 250, 17759)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190959 710087 349824 906824 480883 787145 417279 722370 073919 340070 443401 249434 749641 932901 868196 297304 065183 903919 477002 285883 > 3²⁵⁰ [i]