MinT - Best Known (45, 45+40, s)-Nets in Base 7

Best Known (45, 45+40, s)-Nets in Base 7

(45, 45+40, 104)-Net over F₇ — Constructive and digital

Digital (45, 85, 104)-net over F₇, using

1 times m-reduction [i] based on digital (45, 86, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 43, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(45, 45+40, 168)-Net over F₇ — Digital

Digital (45, 85, 168)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+40, 5392)-Net in Base 7 — Upper bound on s

There is no (45, 85, 5393)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 682554 795553 561280 074816 789530 466355 630011 841172 488861 559451 176168 983137 > 7⁸⁵ [i]