MinT - Best Known (222−66, 222, s)-Nets in Base 3

Best Known (222−66, 222, s)-Nets in Base 3

(222−66, 222, 252)-Net over F₃ — Constructive and digital

Digital (156, 222, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 74, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(222−66, 222, 500)-Net over F₃ — Digital

Digital (156, 222, 500)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−66, 222, 10634)-Net in Base 3 — Upper bound on s

There is no (156, 222, 10635)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8342 883589 471169 748174 579397 000056 485248 895165 566482 203759 060957 610825 817612 935279 015772 333151 978313 798615 > 3²²² [i]