MinT - Best Known (137, 137+46, s)-Nets in Base 3

Best Known (137, 137+46, s)-Nets in Base 3

(137, 137+46, 288)-Net over F₃ — Constructive and digital

Digital (137, 183, 288)-net over F₃, using

6 times m-reduction [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]

(137, 137+46, 774)-Net over F₃ — Digital

Digital (137, 183, 774)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+46, 29465)-Net in Base 3 — Upper bound on s

There is no (137, 183, 29466)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2056 859942 315935 029679 573769 856821 159123 636563 776648 738742 385312 945239 406653 951093 073001 > 3¹⁸³ [i]