MinT - Best Known (86, 86+62, s)-Nets in Base 3

Best Known (86, 86+62, s)-Nets in Base 3

(86, 86+62, 80)-Net over F₃ — Constructive and digital

Digital (86, 148, 80)-net over F₃, using

8 times m-reduction [i] based on digital (86, 156, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 78, 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]

(86, 86+62, 127)-Net over F₃ — Digital

Digital (86, 148, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+62, 1147)-Net in Base 3 — Upper bound on s

There is no (86, 148, 1148)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 42112 349227 039618 353203 938662 896644 472810 534868 440603 320171 264068 599121 > 3¹⁴⁸ [i]