MinT - Best Known (175−45, 175, s)-Nets in Base 3

Best Known (175−45, 175, s)-Nets in Base 3

(175−45, 175, 288)-Net over F₃ — Constructive and digital

Digital (130, 175, 288)-net over F₃, using

t-expansion [i] based on digital (129, 175, 288)-net over F₃, using
- 2 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]

(175−45, 175, 683)-Net over F₃ — Digital

Digital (130, 175, 683)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−45, 175, 26857)-Net in Base 3 — Upper bound on s

There is no (130, 175, 26858)-net in base 3, because

1 times m-reduction [i] would yield (130, 174, 26858)-net in base 3, but
- 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]