MinT - Best Known (57−35, 57, s)-Nets in Base 7

Best Known (57−35, 57, s)-Nets in Base 7

(57−35, 57, 29)-Net over F₇ — Constructive and digital

Digital (22, 57, 29)-net over F₇, using

t-expansion [i] based on digital (21, 57, 29)-net over F₇, using
- net from sequence [i] based on digital (21, 28)-sequence over F₇, using
  - Niederreiter sequence [i]

(57−35, 57, 72)-Net over F₇ — Digital

Digital (22, 57, 72)-net over F₇, using

net from sequence [i] based on digital (22, 71)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
  - an algebraic function field over â„¤₇ by Yeo [i]

(57−35, 57, 716)-Net in Base 7 — Upper bound on s

There is no (22, 57, 717)-net in base 7, because

1 times m-reduction [i] would yield (22, 56, 717)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 214542 443881 460496 251945 616557 213605 696811 454799 > 7⁵⁶ [i]