MinT - Best Known (160, 160+74, s)-Nets in Base 3

Best Known (160, 160+74, s)-Nets in Base 3

(160, 160+74, 192)-Net over F₃ — Constructive and digital

Digital (160, 234, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 78, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(160, 160+74, 430)-Net over F₃ — Digital

Digital (160, 234, 430)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160, 160+74, 7590)-Net in Base 3 — Upper bound on s

There is no (160, 234, 7591)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4439 782380 316689 221384 497132 790902 891469 431221 299595 803748 291777 377507 289024 258439 110495 184896 992252 203166 626887 > 3²³⁴ [i]