MinT - Best Known (13, 13+85, s)-Nets in Base 7

Best Known (13, 13+85, s)-Nets in Base 7

(13, 13+85, 21)-Net over F₇ — Constructive and digital

Digital (13, 98, 21)-net over F₇, using

net from sequence [i] based on digital (13, 20)-sequence over F₇, using
- Niederreiter sequence [i]

(13, 13+85, 48)-Net over F₇ — Digital

Digital (13, 98, 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]

(13, 13+85, 97)-Net in Base 7 — Upper bound on s

There is no (13, 98, 98)-net in base 7, because

11 times m-reduction [i] would yield (13, 87, 98)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁸⁷, 98, S₇, 74), but
  - the linear programming bound shows that MÂ â‰¥ 42407 610952 566807 294788 235072 104256 021156 669481 359079 294981 146935 094240 996998 497183 / 1146 522975 > 7⁸⁷ [i]