Best Known (135−126, 135, s)-Nets in Base 8
(135−126, 135, 45)-Net over F8 — Constructive and digital
Digital (9, 135, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
(135−126, 135, 79)-Net over F8 — Upper bound on s (digital)
There is no digital (9, 135, 80)-net over F8, because
- 62 times m-reduction [i] would yield digital (9, 73, 80)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(873, 80, F8, 64) (dual of [80, 7, 65]-code), but
- residual code [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(873, 80, F8, 64) (dual of [80, 7, 65]-code), but
(135−126, 135, 81)-Net in Base 8 — Upper bound on s
There is no (9, 135, 82)-net in base 8, because
- 63 times m-reduction [i] would yield (9, 72, 82)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(872, 82, S8, 63), but
- the linear programming bound shows that M ≥ 5 943562 882293 362898 492495 479069 260758 679371 222248 872068 611620 811931 910144 / 44 417945 > 872 [i]
- extracting embedded orthogonal array [i] would yield OA(872, 82, S8, 63), but