MinT - Best Known (144, 144+57, s)-Nets in Base 3

Best Known (144, 144+57, s)-Nets in Base 3

(144, 144+57, 282)-Net over F₃ — Constructive and digital

Digital (144, 201, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 67, 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]

(144, 144+57, 536)-Net over F₃ — Digital

Digital (144, 201, 536)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+57, 14426)-Net in Base 3 — Upper bound on s

There is no (144, 201, 14427)-net in base 3, because

1 times m-reduction [i] would yield (144, 200, 14427)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265929 632669 146112 477213 022794 690884 699933 610193 729029 350839 296733 636446 071319 286322 942985 263017 > 3²⁰⁰ [i]