MinT - Best Known (154, 154+69, s)-Nets in Base 3

Best Known (154, 154+69, s)-Nets in Base 3

(154, 154+69, 204)-Net over F₃ — Constructive and digital

Digital (154, 223, 204)-net over F₃, using

3¹ times duplication [i] based on digital (153, 222, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 74, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(154, 154+69, 442)-Net over F₃ — Digital

Digital (154, 223, 442)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+69, 8792)-Net in Base 3 — Upper bound on s

There is no (154, 223, 8793)-net in base 3, because

1 times m-reduction [i] would yield (154, 222, 8793)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8347 884677 034335 920179 402945 190467 004461 565708 405291 311537 084089 352173 885980 087460 644128 184533 594182 017145 > 3²²² [i]