MinT - Best Known (250−106, 250, s)-Nets in Base 3

Best Known (250−106, 250, s)-Nets in Base 3

(250−106, 250, 148)-Net over F₃ — Constructive and digital

Digital (144, 250, 148)-net over F₃, using

t-expansion [i] based on digital (142, 250, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(250−106, 250, 193)-Net over F₃ — Digital

Digital (144, 250, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−106, 250, 1781)-Net in Base 3 — Upper bound on s

There is no (144, 250, 1782)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 191583 954873 933933 094338 682046 906179 474535 284995 416718 125634 902777 702102 809618 737544 620996 503564 347009 818577 585350 535141 > 3²⁵⁰ [i]