MinT - Best Known (41−24, 41, s)-Nets in Base 49

Best Known (41−24, 41, s)-Nets in Base 49

(41−24, 41, 105)-Net over F₄₉ — Constructive and digital

Digital (17, 41, 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, 27, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(41−24, 41, 214)-Net over F₄₉ — Digital

Digital (17, 41, 214)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−24, 41, 65602)-Net in Base 49 — Upper bound on s

There is no (17, 41, 65603)-net in base 49, because

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]