MinT - Best Known (138, 138+52, s)-Nets in Base 3

Best Known (138, 138+52, s)-Nets in Base 3

(138, 138+52, 288)-Net over F₃ — Constructive and digital

Digital (138, 190, 288)-net over F₃, using

3¹ times duplication [i] based on digital (137, 189, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 63, 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]

(138, 138+52, 579)-Net over F₃ — Digital

Digital (138, 190, 579)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+52, 16152)-Net in Base 3 — Upper bound on s

There is no (138, 190, 16153)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 503433 215179 642639 301296 992718 570461 758425 252985 828726 850430 487450 376542 628666 858974 495705 > 3¹⁹⁰ [i]