MinT - Best Known (20, 47, s)-Nets in Base 49

Best Known (20, 47, s)-Nets in Base 49

(20, 47, 107)-Net over F₄₉ — Constructive and digital

Digital (20, 47, 107)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 16, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (4, 31, 54)-net over F₄₉, using
  - net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(20, 47, 263)-Net over F₄₉ — Digital

Digital (20, 47, 263)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 47, 112936)-Net in Base 49 — Upper bound on s

There is no (20, 47, 112937)-net in base 49, because

1 times m-reduction [i] would yield (20, 46, 112937)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 561100 240997 300998 620749 637470 583338 657714 862447 205799 274305 796928 305263 901169 > 49⁴⁶ [i]