MinT - Best Known (40, 40+35, s)-Nets in Base 7

Best Known (40, 40+35, s)-Nets in Base 7

(40, 40+35, 104)-Net over F₇ — Constructive and digital

Digital (40, 75, 104)-net over F₇, using

1 times m-reduction [i] based on digital (40, 76, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 38, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(40, 40+35, 158)-Net over F₇ — Digital

Digital (40, 75, 158)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+35, 5696)-Net in Base 7 — Upper bound on s

There is no (40, 75, 5697)-net in base 7, because

1 times m-reduction [i] would yield (40, 74, 5697)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 344 751253 378671 317766 527551 434099 965070 986678 214098 645890 046983 > 7⁷⁴ [i]