MinT - Best Known (100−31, 100, s)-Nets in Base 7

Best Known (100−31, 100, s)-Nets in Base 7

(100−31, 100, 208)-Net over F₇ — Constructive and digital

Digital (69, 100, 208)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (19, 34, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 17, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (35, 66, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 33, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉ (see above)

(100−31, 100, 1332)-Net over F₇ — Digital

Digital (69, 100, 1332)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−31, 100, 404810)-Net in Base 7 — Upper bound on s

There is no (69, 100, 404811)-net in base 7, because

1 times m-reduction [i] would yield (69, 99, 404811)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 462068 749671 374622 325870 213361 681124 662957 544904 210289 138878 690602 797748 651921 233863 > 7⁹⁹ [i]