MinT - Best Known (15, 90, s)-Nets in Base 7

Best Known (15, 90, s)-Nets in Base 7

(15, 90, 23)-Net over F₇ — Constructive and digital

Digital (15, 90, 23)-net over F₇, using

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

(15, 90, 48)-Net over F₇ — Digital

Digital (15, 90, 48)-net over F₇, using

t-expansion [i] based on digital (13, 90, 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]

(15, 90, 125)-Net in Base 7 — Upper bound on s

There is no (15, 90, 126)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁰, 126, S₇, 75), but
- the linear programming bound shows that MÂ â‰¥ 1425 565318 616017 200286 592713 744361 293273 664082 148428 033104 769238 744862 064757 226452 457563 171612 690126 450836 248397 045241 / 124114 559735 380884 292873 557181 371740 570613 > 7⁹⁰ [i]