MinT - Best Known (175, 175+67, s)-Nets in Base 3

Best Known (175, 175+67, s)-Nets in Base 3

(175, 175+67, 288)-Net over F₃ — Constructive and digital

Digital (175, 242, 288)-net over F₃, using

4 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 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]

(175, 175+67, 684)-Net over F₃ — Digital

Digital (175, 242, 684)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175, 175+67, 20047)-Net in Base 3 — Upper bound on s

There is no (175, 242, 20048)-net in base 3, because

1 times m-reduction [i] would yield (175, 241, 20048)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 701697 717939 918690 472202 105262 261833 888055 184320 397518 571062 403750 250908 811264 467339 061247 635231 311234 422508 632225 > 3²⁴¹ [i]