Best Known (17, 29, s)-Nets in Base 9
(17, 29, 232)-Net over F9 — Constructive and digital
Digital (17, 29, 232)-net over F9, using
- 1 times m-reduction [i] based on digital (17, 30, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 15, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 15, 116)-net over F81, using
(17, 29, 240)-Net over F9 — Digital
Digital (17, 29, 240)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(929, 240, F9, 12) (dual of [240, 211, 13]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(928, 236, F9, 12) (dual of [236, 208, 13]-code), using
- trace code [i] based on linear OA(8114, 118, F81, 12) (dual of [118, 104, 13]-code), using
- extended algebraic-geometric code AGe(F,105P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
- trace code [i] based on linear OA(8114, 118, F81, 12) (dual of [118, 104, 13]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(928, 236, F9, 12) (dual of [236, 208, 13]-code), using
(17, 29, 15318)-Net in Base 9 — Upper bound on s
There is no (17, 29, 15319)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4711 320511 760782 031810 181969 > 929 [i]