MinT - Best Known (196−63, 196, s)-Nets in Base 3

Best Known (196−63, 196, s)-Nets in Base 3

(196−63, 196, 162)-Net over F₃ — Constructive and digital

Digital (133, 196, 162)-net over F₃, using

6 times m-reduction [i] based on digital (133, 202, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 101, 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]

(196−63, 196, 351)-Net over F₃ — Digital

Digital (133, 196, 351)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−63, 196, 6196)-Net in Base 3 — Upper bound on s

There is no (133, 196, 6197)-net in base 3, because

1 times m-reduction [i] would yield (133, 195, 6197)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1097 739612 848580 617955 343172 064221 111835 027730 448036 256261 245289 810404 616819 172005 684137 814395 > 3¹⁹⁵ [i]