MinT - Best Known (196−89, 196, s)-Nets in Base 3

Best Known (196−89, 196, s)-Nets in Base 3

(196−89, 196, 80)-Net over F₃ — Constructive and digital

Digital (107, 196, 80)-net over F₃, using

2 times m-reduction [i] based on digital (107, 198, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 99, 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]

(196−89, 196, 129)-Net over F₃ — Digital

Digital (107, 196, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−89, 196, 1080)-Net in Base 3 — Upper bound on s

There is no (107, 196, 1081)-net in base 3, because

1 times m-reduction [i] would yield (107, 195, 1081)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1125 234528 018296 880700 609950 579615 999936 083805 477834 156422 284738 133205 484999 395824 916827 089329 > 3¹⁹⁵ [i]