Best Known (217−15, 217, s)-Nets in Base 2
(217−15, 217, 1329442)-Net over F2 — Constructive and digital
Digital (202, 217, 1329442)-net over F2, using
- 22 times duplication [i] based on digital (200, 215, 1329442)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (46, 53, 131071)-net over F2, using
- digital (147, 162, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
(217−15, 217, 2927272)-Net over F2 — Digital
Digital (202, 217, 2927272)-net over F2, using
- 22 times duplication [i] based on digital (200, 215, 2927272)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2215, 2927272, F2, 3, 15) (dual of [(2927272, 3), 8781601, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(253, 131071, F2, 3, 7) (dual of [(131071, 3), 393160, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (46, 53, 131071)-net over F2, using
- linear OOA(2162, 2796201, F2, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 3-folding [i] based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- linear OOA(253, 131071, F2, 3, 7) (dual of [(131071, 3), 393160, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2215, 2927272, F2, 3, 15) (dual of [(2927272, 3), 8781601, 16]-NRT-code), using
(217−15, 217, large)-Net in Base 2 — Upper bound on s
There is no (202, 217, large)-net in base 2, because
- 13 times m-reduction [i] would yield (202, 204, large)-net in base 2, but