Best Known (25−9, 25, s)-Nets in Base 8
(25−9, 25, 208)-Net over F8 — Constructive and digital
Digital (16, 25, 208)-net over F8, using
- 1 times m-reduction [i] based on digital (16, 26, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 13, 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, 13, 104)-net over F64, using
(25−9, 25, 514)-Net in Base 8 — Constructive
(16, 25, 514)-net in base 8, using
- 81 times duplication [i] based on (15, 24, 514)-net in base 8, using
- base change [i] based on digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, using
- base change [i] based on digital (9, 18, 514)-net over F16, using
(25−9, 25, 532)-Net over F8 — Digital
Digital (16, 25, 532)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(825, 532, F8, 9) (dual of [532, 507, 10]-code), using
- 17 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 17 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0) [i] based on linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using
(25−9, 25, 82886)-Net in Base 8 — Upper bound on s
There is no (16, 25, 82887)-net in base 8, because
- 1 times m-reduction [i] would yield (16, 24, 82887)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 4722 478786 318602 139167 > 824 [i]