Best Known (13−6, 13, s)-Nets in Base 8
(13−6, 13, 130)-Net over F8 — Constructive and digital
Digital (7, 13, 130)-net over F8, using
- 1 times m-reduction [i] based on digital (7, 14, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
(13−6, 13, 133)-Net over F8 — Digital
Digital (7, 13, 133)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(813, 133, F8, 6) (dual of [133, 120, 7]-code), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(812, 130, F8, 6) (dual of [130, 118, 7]-code), using
- trace code [i] based on linear OA(646, 65, F64, 6) (dual of [65, 59, 7]-code or 65-arc in PG(5,64)), using
- extended Reed–Solomon code RSe(59,64) [i]
- trace code [i] based on linear OA(646, 65, F64, 6) (dual of [65, 59, 7]-code or 65-arc in PG(5,64)), using
- 2 step Varšamov–Edel lengthening with (ri) = (1, 0) [i] based on linear OA(812, 130, F8, 6) (dual of [130, 118, 7]-code), using
(13−6, 13, 2125)-Net in Base 8 — Upper bound on s
There is no (7, 13, 2126)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 550436 969762 > 813 [i]