MinT - Best Known (199−54, 199, s)-Nets in Base 3

Best Known (199−54, 199, s)-Nets in Base 3

(199−54, 199, 288)-Net over F₃ — Constructive and digital

Digital (145, 199, 288)-net over F₃, using

2 times m-reduction [i] based on digital (145, 201, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 67, 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]

(199−54, 199, 621)-Net over F₃ — Digital

Digital (145, 199, 621)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−54, 199, 17918)-Net in Base 3 — Upper bound on s

There is no (145, 199, 17919)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88637 320268 432699 665040 207258 904397 939463 900143 352581 573172 616215 346702 529504 309763 193601 906635 > 3¹⁹⁹ [i]