MinT - Best Known (69−47, 69, s)-Nets in Base 7

Best Known (69−47, 69, s)-Nets in Base 7

(69−47, 69, 29)-Net over F₇ — Constructive and digital

Digital (22, 69, 29)-net over F₇, using

t-expansion [i] based on digital (21, 69, 29)-net over F₇, using
- net from sequence [i] based on digital (21, 28)-sequence over F₇, using
  - Niederreiter sequence [i]

(69−47, 69, 72)-Net over F₇ — Digital

Digital (22, 69, 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]

(69−47, 69, 480)-Net in Base 7 — Upper bound on s

There is no (22, 69, 481)-net in base 7, because

1 times m-reduction [i] would yield (22, 68, 481)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2984 343055 146106 807571 738058 533351 902776 106553 681695 723639 > 7⁶⁸ [i]