MinT - Best Known (20, 20+35, s)-Nets in Base 49

Best Known (20, 20+35, s)-Nets in Base 49

(20, 20+35, 103)-Net over F₄₉ — Constructive and digital

Digital (20, 55, 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, 37, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(20, 20+35, 149)-Net over F₄₉ — Digital

Digital (20, 55, 149)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 20+35, 34950)-Net in Base 49 — Upper bound on s

There is no (20, 55, 34951)-net in base 49, because

1 times m-reduction [i] would yield (20, 54, 34951)-net in base 49, but
- 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]