MinT - Best Known (169−43, 169, s)-Nets in Base 3

Best Known (169−43, 169, s)-Nets in Base 3

(169−43, 169, 288)-Net over F₃ — Constructive and digital

Digital (126, 169, 288)-net over F₃, using

t-expansion [i] based on digital (125, 169, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (125, 171, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 57, 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]

(169−43, 169, 693)-Net over F₃ — Digital

Digital (126, 169, 693)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−43, 169, 28452)-Net in Base 3 — Upper bound on s

There is no (126, 169, 28453)-net in base 3, because

1 times m-reduction [i] would yield (126, 168, 28453)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 397626 872946 036628 229133 155581 419929 570545 985194 957857 839937 647603 920234 782747 > 3¹⁶⁸ [i]