MinT - Best Known (157−52, 157, s)-Nets in Base 3

Best Known (157−52, 157, s)-Nets in Base 3

(157−52, 157, 156)-Net over F₃ — Constructive and digital

Digital (105, 157, 156)-net over F₃, using

9 times m-reduction [i] based on digital (105, 166, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 83, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(157−52, 157, 266)-Net over F₃ — Digital

Digital (105, 157, 266)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−52, 157, 3986)-Net in Base 3 — Upper bound on s

There is no (105, 157, 3987)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 812 385265 005367 123461 440163 950288 981683 637306 465512 528769 621829 349713 088725 > 3¹⁵⁷ [i]