Best Known (255−34, 255, s)-Nets in Base 2
(255−34, 255, 1927)-Net over F2 — Constructive and digital
Digital (221, 255, 1927)-net over F2, using
- net defined by OOA [i] based on linear OOA(2255, 1927, F2, 34, 34) (dual of [(1927, 34), 65263, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(2255, 32759, F2, 34) (dual of [32759, 32504, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2255, 32767, F2, 34) (dual of [32767, 32512, 35]-code), using
- 1 times truncation [i] based on linear OA(2256, 32768, F2, 35) (dual of [32768, 32512, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 1 times truncation [i] based on linear OA(2256, 32768, F2, 35) (dual of [32768, 32512, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2255, 32767, F2, 34) (dual of [32767, 32512, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(2255, 32759, F2, 34) (dual of [32759, 32504, 35]-code), using
(255−34, 255, 5464)-Net over F2 — Digital
Digital (221, 255, 5464)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2255, 5464, F2, 5, 34) (dual of [(5464, 5), 27065, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2255, 6553, F2, 5, 34) (dual of [(6553, 5), 32510, 35]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2255, 32765, F2, 34) (dual of [32765, 32510, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2255, 32767, F2, 34) (dual of [32767, 32512, 35]-code), using
- 1 times truncation [i] based on linear OA(2256, 32768, F2, 35) (dual of [32768, 32512, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 1 times truncation [i] based on linear OA(2256, 32768, F2, 35) (dual of [32768, 32512, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(2255, 32767, F2, 34) (dual of [32767, 32512, 35]-code), using
- OOA 5-folding [i] based on linear OA(2255, 32765, F2, 34) (dual of [32765, 32510, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(2255, 6553, F2, 5, 34) (dual of [(6553, 5), 32510, 35]-NRT-code), using
(255−34, 255, 235152)-Net in Base 2 — Upper bound on s
There is no (221, 255, 235153)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 57899 554642 374068 286339 828069 730346 803582 517639 198983 318693 638217 183188 719634 > 2255 [i]