MinT - Best Known (8, 8+10, s)-Nets in Base 7

Best Known (8, 8+10, s)-Nets in Base 7

(8, 8+10, 26)-Net over F₇ — Constructive and digital

Digital (8, 18, 26)-net over F₇, using

2 times m-reduction [i] based on digital (8, 20, 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 (1, 13, 13)-net over F₇ (see above)

(8, 8+10, 36)-Net over F₇ — Digital

Digital (8, 18, 36)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(8, 8+10, 475)-Net in Base 7 — Upper bound on s

There is no (8, 18, 476)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1631 056661 464777 > 7¹⁸ [i]