MinT - Best Known (38−23, 38, s)-Nets in Base 49

Best Known (38−23, 38, s)-Nets in Base 49

(38−23, 38, 104)-Net over F₄₉ — Constructive and digital

Digital (15, 38, 104)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 13, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]
2. digital (2, 25, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(38−23, 38, 164)-Net over F₄₉ — Digital

Digital (15, 38, 164)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(38−23, 38, 49537)-Net in Base 49 — Upper bound on s

There is no (15, 38, 49538)-net in base 49, because

1 times m-reduction [i] would yield (15, 37, 49538)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 344 607948 643688 736878 605243 924816 381404 110162 831701 823488 321825 > 49³⁷ [i]