Best Known (197−26, 197, s)-Nets in Base 2
(197−26, 197, 2521)-Net over F2 — Constructive and digital
Digital (171, 197, 2521)-net over F2, using
- t-expansion [i] based on digital (170, 197, 2521)-net over F2, using
- net defined by OOA [i] based on linear OOA(2197, 2521, F2, 27, 27) (dual of [(2521, 27), 67870, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2197, 32774, F2, 27) (dual of [32774, 32577, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2197, 32774, F2, 27) (dual of [32774, 32577, 28]-code), using
- net defined by OOA [i] based on linear OOA(2197, 2521, F2, 27, 27) (dual of [(2521, 27), 67870, 28]-NRT-code), using
(197−26, 197, 6416)-Net over F2 — Digital
Digital (171, 197, 6416)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2197, 6416, F2, 5, 26) (dual of [(6416, 5), 31883, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2197, 6556, F2, 5, 26) (dual of [(6556, 5), 32583, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2197, 6556, F2, 5, 27) (dual of [(6556, 5), 32583, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2197, 32780, F2, 27) (dual of [32780, 32583, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2197, 32784, F2, 27) (dual of [32784, 32587, 28]-code), using
- OOA 5-folding [i] based on linear OA(2197, 32780, F2, 27) (dual of [32780, 32583, 28]-code), using
- strength reduction [i] based on linear OOA(2197, 6556, F2, 5, 27) (dual of [(6556, 5), 32583, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2197, 6556, F2, 5, 26) (dual of [(6556, 5), 32583, 27]-NRT-code), using
(197−26, 197, 206599)-Net in Base 2 — Upper bound on s
There is no (171, 197, 206600)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 200878 279950 939314 771417 554164 618459 372186 765107 419386 271776 > 2197 [i]