Best Known (154, 176, s)-Nets in Base 2
(154, 176, 5957)-Net over F2 — Constructive and digital
Digital (154, 176, 5957)-net over F2, using
- net defined by OOA [i] based on linear OOA(2176, 5957, F2, 22, 22) (dual of [(5957, 22), 130878, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2176, 65527, F2, 22) (dual of [65527, 65351, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 65535, F2, 22) (dual of [65535, 65359, 23]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 65535, F2, 22) (dual of [65535, 65359, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2176, 65527, F2, 22) (dual of [65527, 65351, 23]-code), using
(154, 176, 11192)-Net over F2 — Digital
Digital (154, 176, 11192)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2176, 11192, F2, 5, 22) (dual of [(11192, 5), 55784, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 13107, F2, 5, 22) (dual of [(13107, 5), 65359, 23]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2176, 65535, F2, 22) (dual of [65535, 65359, 23]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(2177, 65536, F2, 23) (dual of [65536, 65359, 24]-code), using
- OOA 5-folding [i] based on linear OA(2176, 65535, F2, 22) (dual of [65535, 65359, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(2176, 13107, F2, 5, 22) (dual of [(13107, 5), 65359, 23]-NRT-code), using
(154, 176, 321715)-Net in Base 2 — Upper bound on s
There is no (154, 176, 321716)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 95781 387144 594117 789783 864029 505391 439188 512704 021958 > 2176 [i]