MinT - Best Known (223−63, 223, s)-Nets in Base 3

Best Known (223−63, 223, s)-Nets in Base 3

(223−63, 223, 288)-Net over F₃ — Constructive and digital

Digital (160, 223, 288)-net over F₃, using

3¹ times duplication [i] based on digital (159, 222, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 74, 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]

(223−63, 223, 594)-Net over F₃ — Digital

Digital (160, 223, 594)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−63, 223, 16180)-Net in Base 3 — Upper bound on s

There is no (160, 223, 16181)-net in base 3, because

1 times m-reduction [i] would yield (160, 222, 16181)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8344 636500 246602 252565 938745 637099 647851 595768 370296 669087 797854 475852 198970 615404 309610 273883 125788 886395 > 3²²² [i]