MinT - Best Known (132−54, 132, s)-Nets in Base 3

Best Known (132−54, 132, s)-Nets in Base 3

(132−54, 132, 80)-Net over F₃ — Constructive and digital

Digital (78, 132, 80)-net over F₃, using

8 times m-reduction [i] based on digital (78, 140, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 70, 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]

(132−54, 132, 124)-Net over F₃ — Digital

Digital (78, 132, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−54, 132, 1148)-Net in Base 3 — Upper bound on s

There is no (78, 132, 1149)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 964 666247 823397 280861 419246 362522 028806 047714 844693 455250 164331 > 3¹³² [i]