MinT - Best Known (137, 137+70, s)-Nets in Base 3

Best Known (137, 137+70, s)-Nets in Base 3

(137, 137+70, 162)-Net over F₃ — Constructive and digital

Digital (137, 207, 162)-net over F₃, using

3 times m-reduction [i] based on digital (137, 210, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 105, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(137, 137+70, 314)-Net over F₃ — Digital

Digital (137, 207, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+70, 4579)-Net in Base 3 — Upper bound on s

There is no (137, 207, 4580)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 583 212062 525609 204085 961994 008021 205735 470980 821705 270609 611409 008338 085294 362433 079962 708768 645041 > 3²⁰⁷ [i]