MinT - Best Known (225−64, 225, s)-Nets in Base 3

Best Known (225−64, 225, s)-Nets in Base 3

(225−64, 225, 288)-Net over F₃ — Constructive and digital

Digital (161, 225, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 75, 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]

(225−64, 225, 585)-Net over F₃ — Digital

Digital (161, 225, 585)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−64, 225, 14443)-Net in Base 3 — Upper bound on s

There is no (161, 225, 14444)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225442 092291 409206 905582 593914 040609 948158 690021 042770 664359 111955 132921 619419 913071 815973 108187 710059 874561 > 3²²⁵ [i]