Best Known (217−14, 217, s)-Nets in Base 2
(217−14, 217, 1460513)-Net over F2 — Constructive and digital
Digital (203, 217, 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, 161, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- digital (49, 56, 262142)-net over F2, using
(217−14, 217, 3756475)-Net over F2 — Digital
Digital (203, 217, 3756475)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2217, 3756475, F2, 2, 14) (dual of [(3756475, 2), 7512733, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2217, 4456444, F2, 2, 14) (dual of [(4456444, 2), 8912671, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(256, 262143, F2, 2, 7) (dual of [(262143, 2), 524230, 8]-NRT-code), using
- linear OOA(2161, 4194301, F2, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 15]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2217, 4456444, F2, 2, 14) (dual of [(4456444, 2), 8912671, 15]-NRT-code), using
(217−14, 217, large)-Net in Base 2 — Upper bound on s
There is no (203, 217, large)-net in base 2, because
- 12 times m-reduction [i] would yield (203, 205, large)-net in base 2, but