MinT - Best Known (138−48, 138, s)-Nets in Base 3

Best Known (138−48, 138, s)-Nets in Base 3

(138−48, 138, 148)-Net over F₃ — Constructive and digital

Digital (90, 138, 148)-net over F₃, using

8 times m-reduction [i] based on digital (90, 146, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 73, 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]

(138−48, 138, 205)-Net over F₃ — Digital

Digital (90, 138, 205)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−48, 138, 2691)-Net in Base 3 — Upper bound on s

There is no (90, 138, 2692)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 698368 575890 791391 106199 596553 059438 386343 746400 122531 901227 462721 > 3¹³⁸ [i]