MinT - Best Known (197−63, 197, s)-Nets in Base 3

Best Known (197−63, 197, s)-Nets in Base 3

(197−63, 197, 162)-Net over F₃ — Constructive and digital

Digital (134, 197, 162)-net over F₃, using

7 times m-reduction [i] based on digital (134, 204, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 102, 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]

(197−63, 197, 359)-Net over F₃ — Digital

Digital (134, 197, 359)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−63, 197, 6420)-Net in Base 3 — Upper bound on s

There is no (134, 197, 6421)-net in base 3, because

1 times m-reduction [i] would yield (134, 196, 6421)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3282 951261 336326 565949 844827 115899 450130 977984 029143 480785 890484 597118 912954 367017 447893 832955 > 3¹⁹⁶ [i]