MinT - Best Known (52−29, 52, s)-Nets in Base 7

Best Known (52−29, 52, s)-Nets in Base 7

(52−29, 52, 30)-Net over F₇ — Constructive and digital

Digital (23, 52, 30)-net over F₇, using

net from sequence [i] based on digital (23, 29)-sequence over F₇, using
- Niederreiter sequence [i]

(52−29, 52, 72)-Net over F₇ — Digital

Digital (23, 52, 72)-net over F₇, using

t-expansion [i] based on digital (22, 52, 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]

(52−29, 52, 1198)-Net in Base 7 — Upper bound on s

There is no (23, 52, 1199)-net in base 7, because

1 times m-reduction [i] would yield (23, 51, 1199)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 12 638630 556718 091529 436149 413270 103446 709517 > 7⁵¹ [i]