MinT - Best Known (226−75, 226, s)-Nets in Base 3

Best Known (226−75, 226, s)-Nets in Base 3

(226−75, 226, 162)-Net over F₃ — Constructive and digital

Digital (151, 226, 162)-net over F₃, using

12 times m-reduction [i] based on digital (151, 238, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 119, 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]

(226−75, 226, 359)-Net over F₃ — Digital

Digital (151, 226, 359)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−75, 226, 5802)-Net in Base 3 — Upper bound on s

There is no (151, 226, 5803)-net in base 3, because

1 times m-reduction [i] would yield (151, 225, 5803)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 226470 259058 503077 897974 773215 306965 886095 925534 478026 507424 489326 287767 341452 945316 724737 282103 295117 679951 > 3²²⁵ [i]