MinT - Best Known (138−50, 138, s)-Nets in Base 3

Best Known (138−50, 138, s)-Nets in Base 3

(138−50, 138, 148)-Net over F₃ — Constructive and digital

Digital (88, 138, 148)-net over F₃, using

4 times m-reduction [i] based on digital (88, 142, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 71, 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]

(138−50, 138, 181)-Net over F₃ — Digital

Digital (88, 138, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−50, 138, 2164)-Net in Base 3 — Upper bound on s

There is no (88, 138, 2165)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696887 969390 376307 186362 204428 443733 461702 950471 867887 655891 975435 > 3¹³⁸ [i]