MinT - Best Known (224−63, 224, s)-Nets in Base 3

Best Known (224−63, 224, s)-Nets in Base 3

(224−63, 224, 288)-Net over F₃ — Constructive and digital

Digital (161, 224, 288)-net over F₃, using

1 times m-reduction [i] based on 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]

(224−63, 224, 605)-Net over F₃ — Digital

Digital (161, 224, 605)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−63, 224, 16765)-Net in Base 3 — Upper bound on s

There is no (161, 224, 16766)-net in base 3, because

1 times m-reduction [i] would yield (161, 223, 16766)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25042 183131 314972 000297 223801 560169 974737 325340 153706 530283 452186 600440 412942 578505 954116 760697 274128 763081 > 3²²³ [i]