Best Known (145, 169, s)-Nets in Base 2
(145, 169, 1366)-Net over F2 — Constructive and digital
Digital (145, 169, 1366)-net over F2, using
- net defined by OOA [i] based on linear OOA(2169, 1366, F2, 24, 24) (dual of [(1366, 24), 32615, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2169, 16392, F2, 24) (dual of [16392, 16223, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 16398, F2, 24) (dual of [16398, 16229, 25]-code), using
- 1 times truncation [i] based on linear OA(2170, 16399, F2, 25) (dual of [16399, 16229, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(2170, 16399, F2, 25) (dual of [16399, 16229, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 16398, F2, 24) (dual of [16398, 16229, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2169, 16392, F2, 24) (dual of [16392, 16223, 25]-code), using
(145, 169, 3279)-Net over F2 — Digital
Digital (145, 169, 3279)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2169, 3279, F2, 5, 24) (dual of [(3279, 5), 16226, 25]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2169, 16395, F2, 24) (dual of [16395, 16226, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 16398, F2, 24) (dual of [16398, 16229, 25]-code), using
- 1 times truncation [i] based on linear OA(2170, 16399, F2, 25) (dual of [16399, 16229, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(2170, 16399, F2, 25) (dual of [16399, 16229, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 16398, F2, 24) (dual of [16398, 16229, 25]-code), using
- OOA 5-folding [i] based on linear OA(2169, 16395, F2, 24) (dual of [16395, 16226, 25]-code), using
(145, 169, 91787)-Net in Base 2 — Upper bound on s
There is no (145, 169, 91788)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 748 320001 690430 141075 685887 858681 232000 789522 552864 > 2169 [i]