MinT - Best Known (190−48, 190, s)-Nets in Base 3

Best Known (190−48, 190, s)-Nets in Base 3

(190−48, 190, 288)-Net over F₃ — Constructive and digital

Digital (142, 190, 288)-net over F₃, using

t-expansion [i] based on digital (141, 190, 288)-net over F₃, using
- 5 times m-reduction [i] based on digital (141, 195, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 65, 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]

(190−48, 190, 782)-Net over F₃ — Digital

Digital (142, 190, 782)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−48, 190, 29322)-Net in Base 3 — Upper bound on s

There is no (142, 190, 29323)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 501558 894412 523918 307988 001618 404910 980469 505036 245787 791921 175005 281394 648974 187040 209489 > 3¹⁹⁰ [i]