MinT - Best Known (125, 125+91, s)-Nets in Base 3

Best Known (125, 125+91, s)-Nets in Base 3

(125, 125+91, 148)-Net over F₃ — Constructive and digital

Digital (125, 216, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 108, 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]

(125, 125+91, 173)-Net over F₃ — Digital

Digital (125, 216, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+91, 1633)-Net in Base 3 — Upper bound on s

There is no (125, 216, 1634)-net in base 3, because

1 times m-reduction [i] would yield (125, 215, 1634)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 840133 122528 624968 593259 914340 919789 204991 227975 056174 280601 192757 221788 167081 289715 429698 624125 306061 > 3²¹⁵ [i]