Best Known (7, 13, s)-Nets in Base 9
(7, 13, 164)-Net over F9 — Constructive and digital
Digital (7, 13, 164)-net over F9, using
- 1 times m-reduction [i] based on digital (7, 14, 164)-net over F9, using
- trace code for nets [i] based on digital (0, 7, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 7, 82)-net over F81, using
(7, 13, 167)-Net over F9 — Digital
Digital (7, 13, 167)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(913, 167, F9, 6) (dual of [167, 154, 7]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(912, 164, F9, 6) (dual of [164, 152, 7]-code), using
- trace code [i] based on linear OA(816, 82, F81, 6) (dual of [82, 76, 7]-code or 82-arc in PG(5,81)), using
- extended Reed–Solomon code RSe(76,81) [i]
- trace code [i] based on linear OA(816, 82, F81, 6) (dual of [82, 76, 7]-code or 82-arc in PG(5,81)), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(912, 164, F9, 6) (dual of [164, 152, 7]-code), using
(7, 13, 3098)-Net in Base 9 — Upper bound on s
There is no (7, 13, 3099)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 543087 405577 > 913 [i]