MinT - Best Known (172−44, 172, s)-Nets in Base 3

Best Known (172−44, 172, s)-Nets in Base 3

(172−44, 172, 288)-Net over F₃ — Constructive and digital

Digital (128, 172, 288)-net over F₃, using

t-expansion [i] based on digital (127, 172, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (127, 174, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 58, 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]

(172−44, 172, 688)-Net over F₃ — Digital

Digital (128, 172, 688)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−44, 172, 24302)-Net in Base 3 — Upper bound on s

There is no (128, 172, 24303)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11610 648396 676354 477286 752635 447143 275708 075735 750946 559028 494803 925638 971304 433717 > 3¹⁷² [i]