MinT - Best Known (144, 144+65, s)-Nets in Base 3

Best Known (144, 144+65, s)-Nets in Base 3

(144, 144+65, 192)-Net over F₃ — Constructive and digital

Digital (144, 209, 192)-net over F₃, using

1 times m-reduction [i] based on digital (144, 210, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 70, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(144, 144+65, 411)-Net over F₃ — Digital

Digital (144, 209, 411)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+65, 8043)-Net in Base 3 — Upper bound on s

There is no (144, 209, 8044)-net in base 3, because

1 times m-reduction [i] would yield (144, 208, 8044)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1746 310385 977806 907640 986614 641330 822111 437980 891427 639348 807462 932260 301647 494377 412057 325033 064705 > 3²⁰⁸ [i]