MinT - Best Known (223−67, 223, s)-Nets in Base 3

Best Known (223−67, 223, s)-Nets in Base 3

(223−67, 223, 246)-Net over F₃ — Constructive and digital

Digital (156, 223, 246)-net over F₃, using

3¹ times duplication [i] based on digital (155, 222, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 74, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(223−67, 223, 485)-Net over F₃ — Digital

Digital (156, 223, 485)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−67, 223, 10634)-Net in Base 3 — Upper bound on s

There is no (156, 223, 10635)-net in base 3, because

1 times m-reduction [i] would yield (156, 222, 10635)-net in base 3, but
- 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]