Best Known (122−98, 122, s)-Nets in Base 3
(122−98, 122, 32)-Net over F3 — Constructive and digital
Digital (24, 122, 32)-net over F3, using
- t-expansion [i] based on digital (21, 122, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(122−98, 122, 80)-Net over F3 — Upper bound on s (digital)
There is no digital (24, 122, 81)-net over F3, because
- 47 times m-reduction [i] would yield digital (24, 75, 81)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(375, 81, F3, 51) (dual of [81, 6, 52]-code), but
(122−98, 122, 81)-Net in Base 3 — Upper bound on s
There is no (24, 122, 82)-net in base 3, because
- 48 times m-reduction [i] would yield (24, 74, 82)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(374, 82, S3, 50), but
- the linear programming bound shows that M ≥ 1133 201025 509985 412089 971278 248938 614941 / 5015 > 374 [i]
- extracting embedded orthogonal array [i] would yield OA(374, 82, S3, 50), but