MinT - Best Known (157−66, 157, s)-Nets in Base 3

Best Known (157−66, 157, s)-Nets in Base 3

(157−66, 157, 80)-Net over F₃ — Constructive and digital

Digital (91, 157, 80)-net over F₃, using

9 times m-reduction [i] based on digital (91, 166, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 83, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(157−66, 157, 132)-Net over F₃ — Digital

Digital (91, 157, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−66, 157, 1193)-Net in Base 3 — Upper bound on s

There is no (91, 157, 1194)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 826 397415 720014 030078 376142 717879 396959 501249 855713 601078 569404 026716 112405 > 3¹⁵⁷ [i]