Best Known (206−15, 206, s)-Nets in Base 2
(206−15, 206, 1214753)-Net over F2 — Constructive and digital
Digital (191, 206, 1214753)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (37, 44, 16382)-net over F2, using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 7, 7) (dual of [(16382, 7), 114630, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(244, 16383, F2, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(244, 16382, F2, 7, 7) (dual of [(16382, 7), 114630, 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 (37, 44, 16382)-net over F2, using
(206−15, 206, 2113533)-Net over F2 — Digital
Digital (191, 206, 2113533)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2206, 2113533, F2, 4, 15) (dual of [(2113533, 4), 8453926, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(244, 16383, F2, 4, 7) (dual of [(16383, 4), 65488, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(244, 16383, F2, 3, 7) (dual of [(16383, 3), 49105, 8]-NRT-code), using
- linear OOA(2162, 2097150, F2, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 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 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- linear OOA(244, 16383, F2, 4, 7) (dual of [(16383, 4), 65488, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(206−15, 206, large)-Net in Base 2 — Upper bound on s
There is no (191, 206, large)-net in base 2, because
- 13 times m-reduction [i] would yield (191, 193, large)-net in base 2, but