MinT - Best Known (169, 169+56, s)-Nets in Base 3

Best Known (169, 169+56, s)-Nets in Base 3

(169, 169+56, 328)-Net over F₃ — Constructive and digital

Digital (169, 225, 328)-net over F₃, using

3¹ times duplication [i] based on digital (168, 224, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 56, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(169, 169+56, 953)-Net over F₃ — Digital

Digital (169, 225, 953)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+56, 38519)-Net in Base 3 — Upper bound on s

There is no (169, 225, 38520)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225211 492828 644640 070462 602671 327980 485583 910597 097259 825793 963397 581077 172160 652646 316132 568722 424934 457793 > 3²²⁵ [i]