MinT - Best Known (42−22, 42, s)-Nets in Base 7

Best Known (42−22, 42, s)-Nets in Base 7

(42−22, 42, 29)-Net over F₇ — Constructive and digital

Digital (20, 42, 29)-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 (8, 30, 16)-net over F₇, using
  - net from sequence [i] based on digital (8, 15)-sequence over F₇, using
    - Niederreiter sequence [i]

(42−22, 42, 67)-Net over F₇ — Digital

Digital (20, 42, 67)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(42−22, 42, 1372)-Net in Base 7 — Upper bound on s

There is no (20, 42, 1373)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 313734 073247 114720 294564 497524 620599 > 7⁴² [i]