Best Known (106−91, 106, s)-Nets in Base 8
(106−91, 106, 65)-Net over F8 — Constructive and digital
Digital (15, 106, 65)-net over F8, using
- t-expansion [i] based on digital (14, 106, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(106−91, 106, 125)-Net in Base 8 — Upper bound on s
There is no (15, 106, 126)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(8106, 126, S8, 91), but
- the linear programming bound shows that M ≥ 293 187232 858468 601478 195121 704673 897819 671593 603287 520903 422450 275883 600667 509529 168717 037019 908153 862692 395005 509632 / 543 414185 869329 742359 > 8106 [i]