MinT - Best Known (180−55, 180, s)-Nets in Base 3

Best Known (180−55, 180, s)-Nets in Base 3

(180−55, 180, 204)-Net over F₃ — Constructive and digital

Digital (125, 180, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 60, 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]

(180−55, 180, 382)-Net over F₃ — Digital

Digital (125, 180, 382)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−55, 180, 7926)-Net in Base 3 — Upper bound on s

There is no (125, 180, 7927)-net in base 3, because

1 times m-reduction [i] would yield (125, 179, 7927)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 459301 196580 861338 261332 377368 597634 291567 229976 980430 114792 212806 777967 091222 576427 > 3¹⁷⁹ [i]