MinT - Best Known (172−68, 172, s)-Nets in Base 3

Best Known (172−68, 172, s)-Nets in Base 3

(172−68, 172, 148)-Net over F₃ — Constructive and digital

Digital (104, 172, 148)-net over F₃, using

2 times m-reduction [i] based on digital (104, 174, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 87, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(172−68, 172, 170)-Net over F₃ — Digital

Digital (104, 172, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−68, 172, 1721)-Net in Base 3 — Upper bound on s

There is no (104, 172, 1722)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11810 290708 326021 979428 354830 187324 182765 303324 478417 680918 675382 172610 428992 614373 > 3¹⁷² [i]