MinT - Best Known (144−43, 144, s)-Nets in Base 3

Best Known (144−43, 144, s)-Nets in Base 3

(144−43, 144, 204)-Net over F₃ — Constructive and digital

Digital (101, 144, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 48, 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]

(144−43, 144, 341)-Net over F₃ — Digital

Digital (101, 144, 341)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−43, 144, 7678)-Net in Base 3 — Upper bound on s

There is no (101, 144, 7679)-net in base 3, because

1 times m-reduction [i] would yield (101, 143, 7679)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 422847 172749 071192 382720 334195 857434 717553 188188 760381 550811 663319 > 3¹⁴³ [i]