MinT - Best Known (24−13, 24, s)-Nets in Base 7

Best Known (24−13, 24, s)-Nets in Base 7

(24−13, 24, 26)-Net over F₇ — Constructive and digital

Digital (11, 24, 26)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 7, 13)-net over F₇, using
  - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
2. digital (4, 17, 13)-net over F₇, using
  - Niederreiter sequence (Bratleyâ€“Foxâ€“Niederreiter implementation) with equidistant coordinate [i]

(24−13, 24, 44)-Net over F₇ — Digital

Digital (11, 24, 44)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(24−13, 24, 862)-Net in Base 7 — Upper bound on s

There is no (11, 24, 863)-net in base 7, because

1 times m-reduction [i] would yield (11, 23, 863)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 27 426554 053042 527901 > 7²³ [i]