MinT - Best Known (78−24, 78, s)-Nets in Base 7

Best Known (78−24, 78, s)-Nets in Base 7

(78−24, 78, 206)-Net over F₇ — Constructive and digital

Digital (54, 78, 206)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (14, 26, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 13, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (28, 52, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 26, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(78−24, 78, 1166)-Net over F₇ — Digital

Digital (54, 78, 1166)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−24, 78, 274369)-Net in Base 7 — Upper bound on s

There is no (54, 78, 274370)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 827294 192297 380817 555337 936776 120145 696025 339035 674740 932885 869209 > 7⁷⁸ [i]