MinT - Best Known (171, 171+69, s)-Nets in Base 3

Best Known (171, 171+69, s)-Nets in Base 3

(171, 171+69, 288)-Net over F₃ — Constructive and digital

Digital (171, 240, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 80, 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]

(171, 171+69, 597)-Net over F₃ — Digital

Digital (171, 240, 597)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+69, 15253)-Net in Base 3 — Upper bound on s

There is no (171, 240, 15254)-net in base 3, because

1 times m-reduction [i] would yield (171, 239, 15254)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 077123 851204 477441 483372 663949 150700 849885 458118 134145 806701 139659 679161 330288 111480 924912 884326 281765 659747 389837 > 3²³⁹ [i]