MinT - Best Known (172−46, 172, s)-Nets in Base 3

Best Known (172−46, 172, s)-Nets in Base 3

(172−46, 172, 288)-Net over F₃ — Constructive and digital

Digital (126, 172, 288)-net over F₃, using

3¹ times duplication [i] based on digital (125, 171, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 57, 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]

(172−46, 172, 580)-Net over F₃ — Digital

Digital (126, 172, 580)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−46, 172, 17414)-Net in Base 3 — Upper bound on s

There is no (126, 172, 17415)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11623 196899 157899 744265 696520 375484 971865 500164 863295 273284 153959 177692 767488 816499 > 3¹⁷² [i]