MinT - Best Known (56, 56+26, s)-Nets in Base 7

Best Known (56, 56+26, s)-Nets in Base 7

(56, 56+26, 204)-Net over F₇ — Constructive and digital

Digital (56, 82, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (15, 28, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 14, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (28, 54, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 27, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(56, 56+26, 1016)-Net over F₇ — Digital

Digital (56, 82, 1016)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+26, 202234)-Net in Base 7 — Upper bound on s

There is no (56, 82, 202235)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1986 305626 716336 990259 859614 182240 368470 404122 572314 852929 861486 055643 > 7⁸² [i]