Best Known (10, 17, s)-Nets in Base 8
(10, 17, 160)-Net over F8 — Constructive and digital
Digital (10, 17, 160)-net over F8, using
- 1 times m-reduction [i] based on digital (10, 18, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 9, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 9, 80)-net over F64, using
(10, 17, 178)-Net over F8 — Digital
Digital (10, 17, 178)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(817, 178, F8, 7) (dual of [178, 161, 8]-code), using
- 15 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0) [i] based on linear OA(816, 162, F8, 7) (dual of [162, 146, 8]-code), using
- trace code [i] based on linear OA(648, 81, F64, 7) (dual of [81, 73, 8]-code), using
- extended algebraic-geometric code AGe(F,73P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- trace code [i] based on linear OA(648, 81, F64, 7) (dual of [81, 73, 8]-code), using
- 15 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0) [i] based on linear OA(816, 162, F8, 7) (dual of [162, 146, 8]-code), using
(10, 17, 17010)-Net in Base 8 — Upper bound on s
There is no (10, 17, 17011)-net in base 8, because
- 1 times m-reduction [i] would yield (10, 16, 17011)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 281 476284 897032 > 816 [i]