MinT - Best Known (114, 162, s)-Nets in Base 3

Best Known (114, 162, s)-Nets in Base 3

(114, 162, 228)-Net over F₃ — Constructive and digital

Digital (114, 162, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 54, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(114, 162, 386)-Net over F₃ — Digital

Digital (114, 162, 386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 162, 8121)-Net in Base 3 — Upper bound on s

There is no (114, 162, 8122)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196790 420688 716343 066041 958595 597191 602652 683086 093862 827924 968743 002343 812977 > 3¹⁶² [i]