MinT - Best Known (199−50, 199, s)-Nets in Base 3

Best Known (199−50, 199, s)-Nets in Base 3

(199−50, 199, 288)-Net over F₃ — Constructive and digital

Digital (149, 199, 288)-net over F₃, using

8 times m-reduction [i] based on digital (149, 207, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 69, 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]

(199−50, 199, 830)-Net over F₃ — Digital

Digital (149, 199, 830)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−50, 199, 31926)-Net in Base 3 — Upper bound on s

There is no (149, 199, 31927)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88589 618244 523971 657301 087422 999904 529240 076429 723180 974800 914110 708337 821087 315305 644426 227007 > 3¹⁹⁹ [i]