Best Known (26−10, 26, s)-Nets in Base 8
(26−10, 26, 208)-Net over F8 — Constructive and digital
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
(26−10, 26, 300)-Net in Base 8 — Constructive
(16, 26, 300)-net in base 8, using
- trace code for nets [i] based on (3, 13, 150)-net in base 64, using
- 1 times m-reduction [i] based on (3, 14, 150)-net in base 64, using
- base change [i] based on digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 12, 150)-net over F128, using
- 1 times m-reduction [i] based on (3, 14, 150)-net in base 64, using
(26−10, 26, 353)-Net over F8 — Digital
Digital (16, 26, 353)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(826, 353, F8, 10) (dual of [353, 327, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 518, F8, 10) (dual of [518, 492, 11]-code), using
- construction XX applied to C1 = C([65,73]), C2 = C([67,74]), C3 = C1 + C2 = C([67,73]), and C∩ = C1 ∩ C2 = C([65,74]) [i] based on
- linear OA(822, 511, F8, 9) (dual of [511, 489, 10]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {65,66,…,73}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(822, 511, F8, 8) (dual of [511, 489, 9]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {67,68,…,74}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {65,66,…,74}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {67,68,…,73}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to C1 = C([65,73]), C2 = C([67,74]), C3 = C1 + C2 = C([67,73]), and C∩ = C1 ∩ C2 = C([65,74]) [i] based on
- discarding factors / shortening the dual code based on linear OA(826, 518, F8, 10) (dual of [518, 492, 11]-code), using
(26−10, 26, 18481)-Net in Base 8 — Upper bound on s
There is no (16, 26, 18482)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 302254 411406 974273 185660 > 826 [i]