MinT - Best Known (162−70, 162, s)-Nets in Base 3

Best Known (162−70, 162, s)-Nets in Base 3

(162−70, 162, 80)-Net over F₃ — Constructive and digital

Digital (92, 162, 80)-net over F₃, using

6 times m-reduction [i] based on digital (92, 168, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 84, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(162−70, 162, 126)-Net over F₃ — Digital

Digital (92, 162, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−70, 162, 1089)-Net in Base 3 — Upper bound on s

There is no (92, 162, 1090)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199305 590990 039343 536118 229981 082470 905741 022456 041882 487116 810441 612460 158993 > 3¹⁶² [i]