MinT - Best Known (225−69, 225, s)-Nets in Base 3

Best Known (225−69, 225, s)-Nets in Base 3

(225−69, 225, 228)-Net over F₃ — Constructive and digital

Digital (156, 225, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 75, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(225−69, 225, 458)-Net over F₃ — Digital

Digital (156, 225, 458)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−69, 225, 9381)-Net in Base 3 — Upper bound on s

There is no (156, 225, 9382)-net in base 3, because

1 times m-reduction [i] would yield (156, 224, 9382)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75067 593117 347225 400576 039167 463187 518560 377603 713895 911653 877953 110615 806771 448500 472660 818307 690203 666285 > 3²²⁴ [i]