MinT - Best Known (134, 184, s)-Nets in Base 3

Best Known (134, 184, s)-Nets in Base 3

(134, 184, 288)-Net over F₃ — Constructive and digital

Digital (134, 184, 288)-net over F₃, using

3¹ times duplication [i] based on digital (133, 183, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 61, 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]

(134, 184, 578)-Net over F₃ — Digital

Digital (134, 184, 578)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 184, 16503)-Net in Base 3 — Upper bound on s

There is no (134, 184, 16504)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6179 172205 856713 577838 893892 992896 389038 550271 618879 016054 403426 627087 471053 157136 422513 > 3¹⁸⁴ [i]