MinT - Best Known (234−84, 234, s)-Nets in Base 3

Best Known (234−84, 234, s)-Nets in Base 3

(234−84, 234, 162)-Net over F₃ — Constructive and digital

Digital (150, 234, 162)-net over F₃, using

2 times m-reduction [i] based on digital (150, 236, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 118, 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]

(234−84, 234, 292)-Net over F₃ — Digital

Digital (150, 234, 292)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−84, 234, 3717)-Net in Base 3 — Upper bound on s

There is no (150, 234, 3718)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4468 100715 249789 557343 237775 525578 911321 984537 688967 365015 890320 227341 496979 169066 390501 742937 194344 583342 754365 > 3²³⁴ [i]