MinT - Best Known (65−20, 65, s)-Nets in Base 7

Best Known (65−20, 65, s)-Nets in Base 7

(65−20, 65, 204)-Net over F₇ — Constructive and digital

Digital (45, 65, 204)-net over F₇, using

1 times m-reduction [i] based on digital (45, 66, 204)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (12, 22, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 11, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
        Niederreiter sequence [i]
  2. digital (23, 44, 102)-net over F₇, using
    - trace code for nets [i] based on digital (1, 22, 51)-net over F₄₉, using
      - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(65−20, 65, 1038)-Net over F₇ — Digital

Digital (45, 65, 1038)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−20, 65, 234936)-Net in Base 7 — Upper bound on s

There is no (45, 65, 234937)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8 538422 691967 432427 628454 130075 231361 492383 727929 592673 > 7⁶⁵ [i]