MinT - Best Known (222−64, 222, s)-Nets in Base 3

Best Known (222−64, 222, s)-Nets in Base 3

(222−64, 222, 282)-Net over F₃ — Constructive and digital

Digital (158, 222, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 74, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(222−64, 222, 552)-Net over F₃ — Digital

Digital (158, 222, 552)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−64, 222, 13026)-Net in Base 3 — Upper bound on s

There is no (158, 222, 13027)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8343 336461 479243 599162 599094 599725 626806 338667 914318 306309 205654 796065 961484 391740 582415 103885 103962 490305 > 3²²² [i]