Best Known (169, 169+24, s)-Nets in Base 2
(169, 169+24, 5462)-Net over F2 — Constructive and digital
Digital (169, 193, 5462)-net over F2, using
- net defined by OOA [i] based on linear OOA(2193, 5462, F2, 24, 24) (dual of [(5462, 24), 130895, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2193, 65544, F2, 24) (dual of [65544, 65351, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-code), using
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2193, 65536, F2, 25) (dual of [65536, 65343, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2193, 65544, F2, 24) (dual of [65544, 65351, 25]-code), using
(169, 169+24, 10925)-Net over F2 — Digital
Digital (169, 193, 10925)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 10925, F2, 6, 24) (dual of [(10925, 6), 65357, 25]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2193, 65550, F2, 24) (dual of [65550, 65357, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-code), using
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2193, 65536, F2, 25) (dual of [65536, 65343, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 17, F2, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(2194, 65553, F2, 25) (dual of [65553, 65359, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 65552, F2, 24) (dual of [65552, 65359, 25]-code), using
- OOA 6-folding [i] based on linear OA(2193, 65550, F2, 24) (dual of [65550, 65357, 25]-code), using
(169, 169+24, 367203)-Net in Base 2 — Upper bound on s
There is no (169, 193, 367204)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12554 523488 335972 249957 964137 028689 097780 659771 405740 011976 > 2193 [i]