Best Known (22, 22+46, s)-Nets in Base 3
(22, 22+46, 32)-Net over F3 — Constructive and digital
Digital (22, 68, 32)-net over F3, using
- t-expansion [i] based on digital (21, 68, 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
(22, 22+46, 73)-Net over F3 — Upper bound on s (digital)
There is no digital (22, 68, 74)-net over F3, because
- 1 times m-reduction [i] would yield digital (22, 67, 74)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
(22, 22+46, 75)-Net in Base 3 — Upper bound on s
There is no (22, 68, 76)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(368, 76, S3, 46), but
- the linear programming bound shows that M ≥ 1 013777 979522 262848 532806 654364 768845 / 3619 > 368 [i]