MinT - Best Known (174−44, 174, s)-Nets in Base 3

Best Known (174−44, 174, s)-Nets in Base 3

(174−44, 174, 288)-Net over F₃ — Constructive and digital

Digital (130, 174, 288)-net over F₃, using

t-expansion [i] based on digital (129, 174, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (129, 177, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 59, 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]

(174−44, 174, 726)-Net over F₃ — Digital

Digital (130, 174, 726)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−44, 174, 26857)-Net in Base 3 — Upper bound on s

There is no (130, 174, 26858)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104509 758981 117078 281327 869229 810263 771340 895304 349022 598468 205934 575001 226579 553229 > 3¹⁷⁴ [i]