MinT - Best Known (16, 104, s)-Nets in Base 7

Best Known (16, 104, s)-Nets in Base 7

(16, 104, 24)-Net over F₇ — Constructive and digital

Digital (16, 104, 24)-net over F₇, using

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

(16, 104, 48)-Net over F₇ — Digital

Digital (16, 104, 48)-net over F₇, using

t-expansion [i] based on digital (13, 104, 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]

(16, 104, 116)-Net in Base 7 — Upper bound on s

There is no (16, 104, 117)-net in base 7, because

3 times m-reduction [i] would yield (16, 101, 117)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7¹⁰¹, 117, S₇, 85), but
  - the linear programming bound shows that MÂ â‰¥ 282440 933792 594517 769101 752440 696107 631724 107791 678677 619445 998537 260035 620690 004218 068710 668914 800949 / 12019 043923 183781 > 7¹⁰¹ [i]