Best Known (7, 7+42, s)-Nets in Base 8
(7, 7+42, 34)-Net over F8 — Constructive and digital
Digital (7, 49, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
(7, 7+42, 109)-Net in Base 8 — Upper bound on s
There is no (7, 49, 110)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(849, 110, S8, 42), but
- the linear programming bound shows that M ≥ 7 655784 716884 671957 007923 903539 115362 582837 836158 934938 054867 701017 743623 022624 225077 617055 760384 / 41913 924997 119687 287821 288383 111187 950672 523296 982075 > 849 [i]