MinT - Best Known (46−40, 46, s)-Nets in Base 7

Best Known (46−40, 46, s)-Nets in Base 7

(46−40, 46, 14)-Net over F₇ — Constructive and digital

Digital (6, 46, 14)-net over F₇, using

net from sequence [i] based on digital (6, 13)-sequence over F₇, using
- Niederreiter sequence [i]

(46−40, 46, 24)-Net over F₇ — Digital

Digital (6, 46, 24)-net over F₇, using

t-expansion [i] based on digital (4, 46, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(46−40, 46, 54)-Net in Base 7 — Upper bound on s

There is no (6, 46, 55)-net in base 7, because

1 times m-reduction [i] would yield (6, 45, 55)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁴⁵, 55, S₇, 39), but
  - the linear programming bound shows that MÂ â‰¥ 7 115210 095838 304031 964199 481495 668125 171851 / 55120 > 7⁴⁵ [i]