MinT - Best Known (185−81, 185, s)-Nets in Base 3

Best Known (185−81, 185, s)-Nets in Base 3

(185−81, 185, 80)-Net over F₃ — Constructive and digital

Digital (104, 185, 80)-net over F₃, using

7 times m-reduction [i] based on digital (104, 192, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 96, 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]

(185−81, 185, 136)-Net over F₃ — Digital

Digital (104, 185, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−81, 185, 1195)-Net in Base 3 — Upper bound on s

There is no (104, 185, 1196)-net in base 3, because

1 times m-reduction [i] would yield (104, 184, 1196)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6251 393051 665103 241081 266516 131523 118705 154428 254018 372160 380803 036531 107994 402250 853057 > 3¹⁸⁴ [i]