MinT - Best Known (46−24, 46, s)-Nets in Base 7

Best Known (46−24, 46, s)-Nets in Base 7

(46−24, 46, 30)-Net over F₇ — Constructive and digital

Digital (22, 46, 30)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 13, 13)-net over F₇, using
  - a shift-net [i]
2. digital (9, 33, 17)-net over F₇, using
  - net from sequence [i] based on digital (9, 16)-sequence over F₇, using
    - Niederreiter sequence [i]

(46−24, 46, 72)-Net over F₇ — Digital

Digital (22, 46, 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]

(46−24, 46, 1522)-Net in Base 7 — Upper bound on s

There is no (22, 46, 1523)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 750 647981 893887 613026 634327 486279 036633 > 7⁴⁶ [i]