MinT - Best Known (41, 41+19, s)-Nets in Base 7

Best Known (41, 41+19, s)-Nets in Base 7

(41, 41+19, 204)-Net over F₇ — Constructive and digital

Digital (41, 60, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (11, 20, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 10, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (21, 40, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 20, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(41, 41+19, 835)-Net over F₇ — Digital

Digital (41, 60, 835)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+19, 239705)-Net in Base 7 — Upper bound on s

There is no (41, 60, 239706)-net in base 7, because

1 times m-reduction [i] would yield (41, 59, 239706)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 72 576838 414045 247424 784133 314644 367512 298448 282893 > 7⁵⁹ [i]