MinT - Best Known (17, 17+25, s)-Nets in Base 49

Best Known (17, 17+25, s)-Nets in Base 49

(17, 17+25, 105)-Net over F₄₉ — Constructive and digital

Digital (17, 42, 105)-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 (3, 28, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(17, 17+25, 194)-Net over F₄₉ — Digital

Digital (17, 42, 194)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(17, 17+25, 65602)-Net in Base 49 — Upper bound on s

There is no (17, 42, 65603)-net in base 49, because

1 times m-reduction [i] would yield (17, 41, 65603)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 1986 547883 275537 231721 543893 855886 361784 361417 372832 879245 846471 754433 > 49⁴¹ [i]