MinT - Best Known (65, 65+30, s)-Nets in Base 7

Best Known (65, 65+30, s)-Nets in Base 7

(65, 65+30, 204)-Net over F₇ — Constructive and digital

Digital (65, 95, 204)-net over F₇, using

1 times m-reduction [i] based on digital (65, 96, 204)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (17, 32, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 16, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (33, 64, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 32, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(65, 65+30, 1156)-Net over F₇ — Digital

Digital (65, 95, 1156)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+30, 240927)-Net in Base 7 — Upper bound on s

There is no (65, 95, 240928)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 192 457631 703007 946994 982125 300180 868852 577626 752621 637985 875222 683466 880217 292033 > 7⁹⁵ [i]