Best Known (218−15, 218, s)-Nets in Base 2
(218−15, 218, 1460513)-Net over F2 — Constructive and digital
Digital (203, 218, 1460513)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (49, 56, 262142)-net over F2, using
- net defined by OOA [i] based on linear OOA(256, 262142, F2, 7, 7) (dual of [(262142, 7), 1834938, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(256, 262143, F2, 3, 7) (dual of [(262143, 3), 786373, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(256, 262142, F2, 7, 7) (dual of [(262142, 7), 1834938, 8]-NRT-code), 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
- digital (49, 56, 262142)-net over F2, using
(218−15, 218, 3058344)-Net over F2 — Digital
Digital (203, 218, 3058344)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2218, 3058344, F2, 3, 15) (dual of [(3058344, 3), 9174814, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(256, 262143, F2, 3, 7) (dual of [(262143, 3), 786373, 8]-NRT-code), 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
- (u, u+v)-construction [i] based on
(218−15, 218, large)-Net in Base 2 — Upper bound on s
There is no (203, 218, large)-net in base 2, because
- 13 times m-reduction [i] would yield (203, 205, large)-net in base 2, but