MinT - Best Known (15, 15+79, s)-Nets in Base 7

Best Known (15, 15+79, s)-Nets in Base 7

(15, 15+79, 23)-Net over F₇ — Constructive and digital

Digital (15, 94, 23)-net over F₇, using

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

(15, 15+79, 48)-Net over F₇ — Digital

Digital (15, 94, 48)-net over F₇, using

t-expansion [i] based on digital (13, 94, 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, 15+79, 114)-Net in Base 7 — Upper bound on s

There is no (15, 94, 115)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁴, 115, S₇, 79), but
- the linear programming bound shows that MÂ â‰¥ 2034 206738 975024 462340 937457 958017 253281 790044 959327 785406 085156 101839 708815 437393 759435 377211 716157 / 46 991071 222638 400000 > 7⁹⁴ [i]