MinT - Best Known (217−74, 217, s)-Nets in Base 3

Best Known (217−74, 217, s)-Nets in Base 3

(217−74, 217, 162)-Net over F₃ — Constructive and digital

Digital (143, 217, 162)-net over F₃, using

5 times m-reduction [i] based on digital (143, 222, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 111, 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]

(217−74, 217, 318)-Net over F₃ — Digital

Digital (143, 217, 318)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−74, 217, 4567)-Net in Base 3 — Upper bound on s

There is no (143, 217, 4568)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 411589 513391 933448 682132 281011 784205 858997 266801 312504 504868 772380 553302 661113 262828 728262 788838 978353 > 3²¹⁷ [i]