MinT - Best Known (106−33, 106, s)-Nets in Base 7

Best Known (106−33, 106, s)-Nets in Base 7

(106−33, 106, 208)-Net over F₇ — Constructive and digital

Digital (73, 106, 208)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (20, 36, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 18, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (37, 70, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 35, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(106−33, 106, 1359)-Net over F₇ — Digital

Digital (73, 106, 1359)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−33, 106, 398411)-Net in Base 7 — Upper bound on s

There is no (73, 106, 398412)-net in base 7, because

1 times m-reduction [i] would yield (73, 105, 398412)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54362 109006 361613 740823 287178 389532 116682 810291 707424 851914 497685 270069 254451 757000 487809 > 7¹⁰⁵ [i]