MinT - Best Known (208−53, 208, s)-Nets in Base 3

Best Known (208−53, 208, s)-Nets in Base 3

(208−53, 208, 288)-Net over F₃ — Constructive and digital

Digital (155, 208, 288)-net over F₃, using

8 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 72, 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]

(208−53, 208, 814)-Net over F₃ — Digital

Digital (155, 208, 814)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−53, 208, 33154)-Net in Base 3 — Upper bound on s

There is no (155, 208, 33155)-net in base 3, because

1 times m-reduction [i] would yield (155, 207, 33155)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 580 917090 316498 673134 652802 756900 686770 316135 086279 692994 565865 400260 670002 275663 625059 446131 225525 > 3²⁰⁷ [i]