MinT - Best Known (19, 52, s)-Nets in Base 49

Best Known (19, 52, s)-Nets in Base 49

(19, 52, 103)-Net over F₄₉ — Constructive and digital

Digital (19, 52, 103)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 17, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 35, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(19, 52, 146)-Net over F₄₉ — Digital

Digital (19, 52, 146)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(19, 52, 34569)-Net in Base 49 — Upper bound on s

There is no (19, 52, 34570)-net in base 49, because

1 times m-reduction [i] would yield (19, 51, 34570)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 158 490981 197476 458747 297695 667239 933606 468014 444649 752083 786843 797698 486126 758133 310977 > 49⁵¹ [i]