MinT - Best Known (237−64, 237, s)-Nets in Base 3

Best Known (237−64, 237, s)-Nets in Base 3

(237−64, 237, 288)-Net over F₃ — Constructive and digital

Digital (173, 237, 288)-net over F₃, using

6 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 81, 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]

(237−64, 237, 733)-Net over F₃ — Digital

Digital (173, 237, 733)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−64, 237, 21822)-Net in Base 3 — Upper bound on s

There is no (173, 237, 21823)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119697 217894 416223 262262 086209 792845 184490 724312 873022 987115 329035 831185 763340 217880 307197 206774 833641 679367 811009 > 3²³⁷ [i]