MinT - Best Known (137, 137+56, s)-Nets in Base 3

Best Known (137, 137+56, s)-Nets in Base 3

(137, 137+56, 252)-Net over F₃ — Constructive and digital

Digital (137, 193, 252)-net over F₃, using

3¹ times duplication [i] based on digital (136, 192, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 64, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(137, 137+56, 479)-Net over F₃ — Digital

Digital (137, 193, 479)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+56, 10955)-Net in Base 3 — Upper bound on s

There is no (137, 193, 10956)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 733009 249998 847915 747164 496607 373977 283705 982656 804529 751794 124272 000314 691887 194339 029313 > 3¹⁹³ [i]