MinT - Best Known (194−51, 194, s)-Nets in Base 3

Best Known (194−51, 194, s)-Nets in Base 3

(194−51, 194, 288)-Net over F₃ — Constructive and digital

Digital (143, 194, 288)-net over F₃, using

4 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 66, 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]

(194−51, 194, 683)-Net over F₃ — Digital

Digital (143, 194, 683)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−51, 194, 24521)-Net in Base 3 — Upper bound on s

There is no (143, 194, 24522)-net in base 3, because

1 times m-reduction [i] would yield (143, 193, 24522)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 121 573550 636271 293409 201511 090942 712133 063541 037096 573204 530837 699155 889093 482251 294777 286693 > 3¹⁹³ [i]