Best Known (192, 217, s)-Nets in Base 2
(192, 217, 21845)-Net over F2 — Constructive and digital
Digital (192, 217, 21845)-net over F2, using
- net defined by OOA [i] based on linear OOA(2217, 21845, F2, 25, 25) (dual of [(21845, 25), 545908, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2217, 262141, F2, 25) (dual of [262141, 261924, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2217, 262141, F2, 25) (dual of [262141, 261924, 26]-code), using
(192, 217, 37449)-Net over F2 — Digital
Digital (192, 217, 37449)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2217, 37449, F2, 7, 25) (dual of [(37449, 7), 261926, 26]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2217, 262143, F2, 25) (dual of [262143, 261926, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using
- OOA 7-folding [i] based on linear OA(2217, 262143, F2, 25) (dual of [262143, 261926, 26]-code), using
(192, 217, 1386423)-Net in Base 2 — Upper bound on s
There is no (192, 217, 1386424)-net in base 2, because
- 1 times m-reduction [i] would yield (192, 216, 1386424)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 105312 914007 915582 569477 236530 994111 239258 654281 678023 678267 426714 > 2216 [i]