MinT - Best Known (44−27, 44, s)-Nets in Base 49

Best Known (44−27, 44, s)-Nets in Base 49

(44−27, 44, 104)-Net over F₄₉ — Constructive and digital

Digital (17, 44, 104)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 15, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 29, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(44−27, 44, 162)-Net over F₄₉ — Digital

Digital (17, 44, 162)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−27, 44, 45999)-Net in Base 49 — Upper bound on s

There is no (17, 44, 46000)-net in base 49, because

1 times m-reduction [i] would yield (17, 43, 46000)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 4 769547 288368 214389 955669 346365 922155 846793 326757 844041 163057 611160 505601 > 49⁴³ [i]