MinT - Best Known (55, 55+25, s)-Nets in Base 7

Best Known (55, 55+25, s)-Nets in Base 7

(55, 55+25, 206)-Net over F₇ — Constructive and digital

Digital (55, 80, 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 (29, 54, 104)-net over F₇, using
  - trace code for nets [i] based on digital (2, 27, 52)-net over F₄₉, using
    - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(55, 55+25, 1084)-Net over F₇ — Digital

Digital (55, 80, 1084)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+25, 322672)-Net in Base 7 — Upper bound on s

There is no (55, 80, 322673)-net in base 7, because

1 times m-reduction [i] would yield (55, 79, 322673)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 790961 721198 970969 991304 132799 727905 201784 588273 172375 396541 827233 > 7⁷⁹ [i]