MinT - Best Known (190−51, 190, s)-Nets in Base 3

Best Known (190−51, 190, s)-Nets in Base 3

(190−51, 190, 288)-Net over F₃ — Constructive and digital

Digital (139, 190, 288)-net over F₃, using

2 times m-reduction [i] based on digital (139, 192, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 64, 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]

(190−51, 190, 621)-Net over F₃ — Digital

Digital (139, 190, 621)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−51, 190, 20564)-Net in Base 3 — Upper bound on s

There is no (139, 190, 20565)-net in base 3, because

1 times m-reduction [i] would yield (139, 189, 20565)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 500523 476718 038345 185225 835259 950301 227826 815717 997046 718096 663975 352702 799066 136754 676427 > 3¹⁸⁹ [i]