MinT - Best Known (70−22, 70, s)-Nets in Base 7

Best Known (70−22, 70, s)-Nets in Base 7

(70−22, 70, 204)-Net over F₇ — Constructive and digital

Digital (48, 70, 204)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (13, 24, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 12, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]
2. digital (24, 46, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 23, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉ (see above)

(70−22, 70, 960)-Net over F₇ — Digital

Digital (48, 70, 960)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−22, 70, 195318)-Net in Base 7 — Upper bound on s

There is no (48, 70, 195319)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143504 188968 717372 375240 160205 702731 751279 161886 365513 465855 > 7⁷⁰ [i]