MinT - Best Known (86−23, 86, s)-Nets in Base 3

Best Known (86−23, 86, s)-Nets in Base 3

(86−23, 86, 204)-Net over F₃ — Constructive and digital

Digital (63, 86, 204)-net over F₃, using

1 times m-reduction [i] based on digital (63, 87, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 29, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(86−23, 86, 342)-Net over F₃ — Digital

Digital (63, 86, 342)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−23, 86, 11924)-Net in Base 3 — Upper bound on s

There is no (63, 86, 11925)-net in base 3, because

1 times m-reduction [i] would yield (63, 85, 11925)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35926 877425 589402 443195 959463 696500 408011 > 3⁸⁵ [i]