MinT - Best Known (106−91, 106, s)-Nets in Base 7

Best Known (106−91, 106, s)-Nets in Base 7

(106−91, 106, 23)-Net over F₇ — Constructive and digital

Digital (15, 106, 23)-net over F₇, using

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

(106−91, 106, 48)-Net over F₇ — Digital

Digital (15, 106, 48)-net over F₇, using

t-expansion [i] based on digital (13, 106, 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]

(106−91, 106, 109)-Net in Base 7 — Upper bound on s

There is no (15, 106, 110)-net in base 7, because

7 times m-reduction [i] would yield (15, 99, 110)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁹⁹, 110, S₇, 84), but
  - the linear programming bound shows that MÂ â‰¥ 1760 091261 324378 929559 119960 831347 616737 731471 918661 084961 859631 948665 704893 020113 817143 785727 / 3453 329204 > 7⁹⁹ [i]