MinT - Best Known (54−34, 54, s)-Nets in Base 49

Best Known (54−34, 54, s)-Nets in Base 49

(54−34, 54, 103)-Net over F₄₉ — Constructive and digital

Digital (20, 54, 103)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 18, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 36, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(54−34, 54, 157)-Net over F₄₉ — Digital

Digital (20, 54, 157)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−34, 54, 34950)-Net in Base 49 — Upper bound on s

There is no (20, 54, 34951)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 18 647054 770743 162868 237066 277379 420369 873898 602494 756685 008474 626299 273671 866895 208246 742609 > 49⁵⁴ [i]