MinT - Best Known (18, 47, s)-Nets in Base 49

Best Known (18, 47, s)-Nets in Base 49

(18, 47, 104)-Net over F₄₉ — Constructive and digital

Digital (18, 47, 104)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 16, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 31, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(18, 47, 163)-Net over F₄₉ — Digital

Digital (18, 47, 163)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 47, 45045)-Net in Base 49 — Upper bound on s

There is no (18, 47, 45046)-net in base 49, because

1 times m-reduction [i] would yield (18, 46, 45046)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 561142 080415 655914 974305 907810 585924 664916 474013 221181 306024 055707 243411 791041 > 49⁴⁶ [i]