MinT - Best Known (41−22, 41, s)-Nets in Base 7

Best Known (41−22, 41, s)-Nets in Base 7

(41−22, 41, 28)-Net over F₇ — Constructive and digital

Digital (19, 41, 28)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 12, 13)-net over F₇, using
  - 1 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
2. digital (7, 29, 15)-net over F₇, using
  - net from sequence [i] based on digital (7, 14)-sequence over F₇, using
    - Niederreiter sequence [i]

(41−22, 41, 60)-Net over F₇ — Digital

Digital (19, 41, 60)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−22, 41, 1148)-Net in Base 7 — Upper bound on s

There is no (19, 41, 1149)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 44699 164988 668092 265961 443803 022135 > 7⁴¹ [i]