MinT - Best Known (103, 103+70, s)-Nets in Base 3

Best Known (103, 103+70, s)-Nets in Base 3

(103, 103+70, 128)-Net over F₃ — Constructive and digital

Digital (103, 173, 128)-net over F₃, using

7 times m-reduction [i] based on digital (103, 180, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 90, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(103, 103+70, 160)-Net over F₃ — Digital

Digital (103, 173, 160)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+70, 1552)-Net in Base 3 — Upper bound on s

There is no (103, 173, 1553)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34981 175143 063855 254112 990418 357959 197602 463506 968910 013406 255920 635248 928982 455643 > 3¹⁷³ [i]