Best Known (206, 220, s)-Nets in Base 2
(206, 220, 1722658)-Net over F2 — Constructive and digital
Digital (206, 220, 1722658)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (52, 59, 524287)-net over F2, 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
(206, 220, 4538161)-Net over F2 — Digital
Digital (206, 220, 4538161)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2220, 4538161, F2, 2, 14) (dual of [(4538161, 2), 9076102, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2220, 4718588, F2, 2, 14) (dual of [(4718588, 2), 9436956, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(259, 524287, F2, 2, 7) (dual of [(524287, 2), 1048515, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (52, 59, 524287)-net over F2, 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
- linear OOA(259, 524287, F2, 2, 7) (dual of [(524287, 2), 1048515, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2220, 4718588, F2, 2, 14) (dual of [(4718588, 2), 9436956, 15]-NRT-code), using
(206, 220, large)-Net in Base 2 — Upper bound on s
There is no (206, 220, large)-net in base 2, because
- 12 times m-reduction [i] would yield (206, 208, large)-net in base 2, but