MinT - Best Known (146, 146+57, s)-Nets in Base 3

Best Known (146, 146+57, s)-Nets in Base 3

(146, 146+57, 282)-Net over F₃ — Constructive and digital

Digital (146, 203, 282)-net over F₃, using

1 times m-reduction [i] based on digital (146, 204, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 68, 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]

(146, 146+57, 559)-Net over F₃ — Digital

Digital (146, 203, 559)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+57, 15606)-Net in Base 3 — Upper bound on s

There is no (146, 203, 15607)-net in base 3, because

1 times m-reduction [i] would yield (146, 202, 15607)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 393510 055408 190202 740545 633900 371856 982551 414792 495609 666189 451983 061709 556263 087147 636779 215561 > 3²⁰² [i]