MinT - Best Known (86, 86+43, s)-Nets in Base 3

Best Known (86, 86+43, s)-Nets in Base 3

(86, 86+43, 148)-Net over F₃ — Constructive and digital

Digital (86, 129, 148)-net over F₃, using

9 times m-reduction [i] based on digital (86, 138, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 69, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(86, 86+43, 221)-Net over F₃ — Digital

Digital (86, 129, 221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+43, 3492)-Net in Base 3 — Upper bound on s

There is no (86, 129, 3493)-net in base 3, because

1 times m-reduction [i] would yield (86, 128, 3493)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 849379 870111 435233 328437 790588 639037 454097 144230 928940 909851 > 3¹²⁸ [i]