Best Known (26−9, 26, s)-Nets in Base 8
(26−9, 26, 260)-Net over F8 — Constructive and digital
Digital (17, 26, 260)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 8, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 4, 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, 4, 65)-net over F64, using
- digital (9, 18, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- digital (4, 8, 130)-net over F8, using
(26−9, 26, 514)-Net in Base 8 — Constructive
(17, 26, 514)-net in base 8, using
- 82 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
(26−9, 26, 569)-Net over F8 — Digital
Digital (17, 26, 569)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(826, 569, F8, 9) (dual of [569, 543, 10]-code), using
- 53 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 35 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]
- 53 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 35 times 0) [i] based on linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using
(26−9, 26, 139399)-Net in Base 8 — Upper bound on s
There is no (17, 26, 139400)-net in base 8, because
- 1 times m-reduction [i] would yield (17, 25, 139400)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 37779 641008 470384 200451 > 825 [i]