MinT - Best Known (85−72, 85, s)-Nets in Base 7

Best Known (85−72, 85, s)-Nets in Base 7

(85−72, 85, 21)-Net over F₇ — Constructive and digital

Digital (13, 85, 21)-net over F₇, using

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

(85−72, 85, 48)-Net over F₇ — Digital

Digital (13, 85, 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]

(85−72, 85, 99)-Net in Base 7 — Upper bound on s

There is no (13, 85, 100)-net in base 7, because

1 times m-reduction [i] would yield (13, 84, 100)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁸⁴, 100, S₇, 71), but
  - the linear programming bound shows that MÂ â‰¥ 586479 343942 250094 237706 223891 544580 901593 119460 709506 738817 911019 661869 939740 181983 / 5 014371 735568 > 7⁸⁴ [i]