MinT - Best Known (232−77, 232, s)-Nets in Base 3

Best Known (232−77, 232, s)-Nets in Base 3

(232−77, 232, 162)-Net over F₃ — Constructive and digital

Digital (155, 232, 162)-net over F₃, using

14 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 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]

(232−77, 232, 367)-Net over F₃ — Digital

Digital (155, 232, 367)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−77, 232, 5935)-Net in Base 3 — Upper bound on s

There is no (155, 232, 5936)-net in base 3, because

1 times m-reduction [i] would yield (155, 231, 5936)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 833567 299935 631864 214151 113059 860603 676327 539830 146321 389779 737035 247081 700857 654744 266823 421279 314387 836193 > 3²³¹ [i]