MinT - Best Known (196−77, 196, s)-Nets in Base 3

Best Known (196−77, 196, s)-Nets in Base 3

(196−77, 196, 148)-Net over F₃ — Constructive and digital

Digital (119, 196, 148)-net over F₃, using

8 times m-reduction [i] based on digital (119, 204, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 102, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(196−77, 196, 193)-Net over F₃ — Digital

Digital (119, 196, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−77, 196, 2072)-Net in Base 3 — Upper bound on s

There is no (119, 196, 2073)-net in base 3, because

1 times m-reduction [i] would yield (119, 195, 2073)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1109 450825 923798 542999 649496 500040 322513 324339 527909 192466 225013 968725 192382 697110 258493 782857 > 3¹⁹⁵ [i]