MinT - Best Known (113, 113+70, s)-Nets in Base 3

Best Known (113, 113+70, s)-Nets in Base 3

(113, 113+70, 148)-Net over F₃ — Constructive and digital

Digital (113, 183, 148)-net over F₃, using

9 times m-reduction [i] based on digital (113, 192, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 96, 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]

(113, 113+70, 197)-Net over F₃ — Digital

Digital (113, 183, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+70, 2137)-Net in Base 3 — Upper bound on s

There is no (113, 183, 2138)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2059 787104 400705 992365 342255 664059 946733 814851 782176 564879 012497 354085 718951 000606 837041 > 3¹⁸³ [i]