MinT - Best Known (99−83, 99, s)-Nets in Base 7

Best Known (99−83, 99, s)-Nets in Base 7

(99−83, 99, 24)-Net over F₇ — Constructive and digital

Digital (16, 99, 24)-net over F₇, using

net from sequence [i] based on digital (16, 23)-sequence over F₇, using
- Niederreiter sequence [i]

(99−83, 99, 48)-Net over F₇ — Digital

Digital (16, 99, 48)-net over F₇, using

t-expansion [i] based on digital (13, 99, 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]

(99−83, 99, 119)-Net in Base 7 — Upper bound on s

There is no (16, 99, 120)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁹, 120, S₇, 83), but
- the linear programming bound shows that MÂ â‰¥ 2 089110 638781 217176 556893 626163 995308 412796 076049 090715 116884 748403 899920 357505 493965 540874 965855 092253 / 3 709431 105415 978800 > 7⁹⁹ [i]