MinT - Best Known (234−67, 234, s)-Nets in Base 3

Best Known (234−67, 234, s)-Nets in Base 3

(234−67, 234, 288)-Net over F₃ — Constructive and digital

Digital (167, 234, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 78, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(234−67, 234, 592)-Net over F₃ — Digital

Digital (167, 234, 592)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−67, 234, 15352)-Net in Base 3 — Upper bound on s

There is no (167, 234, 15353)-net in base 3, because

1 times m-reduction [i] would yield (167, 233, 15353)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1478 974760 415158 165438 091346 870903 163587 976508 919728 207236 635064 269067 554445 289109 807743 138437 615547 315060 099443 > 3²³³ [i]