Best Known (29, 29+20, s)-Nets in Base 8
(29, 29+20, 208)-Net over F8 — Constructive and digital
Digital (29, 49, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (29, 52, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 26, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 26, 104)-net over F64, using
(29, 29+20, 258)-Net in Base 8 — Constructive
(29, 49, 258)-net in base 8, using
- 1 times m-reduction [i] based on (29, 50, 258)-net in base 8, using
- trace code for nets [i] based on (4, 25, 129)-net in base 64, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 24, 129)-net over F128, using
- 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- trace code for nets [i] based on (4, 25, 129)-net in base 64, using
(29, 29+20, 264)-Net over F8 — Digital
Digital (29, 49, 264)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(849, 264, F8, 20) (dual of [264, 215, 21]-code), using
- 5 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0) [i] based on linear OA(848, 258, F8, 20) (dual of [258, 210, 21]-code), using
- trace code [i] based on linear OA(6424, 129, F64, 20) (dual of [129, 105, 21]-code), using
- extended algebraic-geometric code AGe(F,108P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6424, 129, F64, 20) (dual of [129, 105, 21]-code), using
- 5 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0) [i] based on linear OA(848, 258, F8, 20) (dual of [258, 210, 21]-code), using
(29, 29+20, 17213)-Net in Base 8 — Upper bound on s
There is no (29, 49, 17214)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 178 455795 202045 459035 084266 360446 598839 464642 > 849 [i]