MinT - Best Known (18, 51, s)-Nets in Base 49

Best Known (18, 51, s)-Nets in Base 49

(18, 51, 102)-Net over F₄₉ — Constructive and digital

Digital (18, 51, 102)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 17, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (1, 34, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(18, 51, 128)-Net over F₄₉ — Digital

Digital (18, 51, 128)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 51, 27104)-Net in Base 49 — Upper bound on s

There is no (18, 51, 27105)-net in base 49, because

1 times m-reduction [i] would yield (18, 50, 27105)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 3 236223 819659 520870 416056 569553 523135 948102 755850 964769 811933 701761 298304 256181 033729 > 49⁵⁰ [i]