MinT - Best Known (92−77, 92, s)-Nets in Base 7

Best Known (92−77, 92, s)-Nets in Base 7

(92−77, 92, 23)-Net over F₇ — Constructive and digital

Digital (15, 92, 23)-net over F₇, using

net from sequence [i] based on digital (15, 22)-sequence over F₇, using
- Niederreiter sequence [i]

(92−77, 92, 48)-Net over F₇ — Digital

Digital (15, 92, 48)-net over F₇, using

t-expansion [i] based on digital (13, 92, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(92−77, 92, 116)-Net in Base 7 — Upper bound on s

There is no (15, 92, 117)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹², 117, S₇, 77), but
- the linear programming bound shows that MÂ â‰¥ 57154 995877 421430 549280 856087 757953 474621 064848 837707 496864 103710 553374 879110 654571 653522 209967 070483 / 101106 457630 688664 657360 > 7⁹² [i]