MinT - Best Known (204−59, 204, s)-Nets in Base 3

Best Known (204−59, 204, s)-Nets in Base 3

(204−59, 204, 264)-Net over F₃ — Constructive and digital

Digital (145, 204, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 68, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(204−59, 204, 508)-Net over F₃ — Digital

Digital (145, 204, 508)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−59, 204, 12734)-Net in Base 3 — Upper bound on s

There is no (145, 204, 12735)-net in base 3, because

1 times m-reduction [i] would yield (145, 203, 12735)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 185029 218788 652660 336710 556133 058471 037281 302466 955564 276338 755481 335744 709293 563446 035215 095111 > 3²⁰³ [i]