MinT - Best Known (40−24, 40, s)-Nets in Base 49

Best Known (40−24, 40, s)-Nets in Base 49

(40−24, 40, 104)-Net over F₄₉ — Constructive and digital

Digital (16, 40, 104)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 14, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 26, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(40−24, 40, 179)-Net over F₄₉ — Digital

Digital (16, 40, 179)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(40−24, 40, 47430)-Net in Base 49 — Upper bound on s

There is no (16, 40, 47431)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 40 544970 597022 898306 216614 016917 824264 327926 878721 457663 976674 531265 > 49⁴⁰ [i]