Best Known (208−14, 208, s)-Nets in Base 2
(208−14, 208, 1231137)-Net over F2 — Constructive and digital
Digital (194, 208, 1231137)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (40, 47, 32766)-net over F2, using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 7, 7) (dual of [(32766, 7), 229315, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 7, 7) (dual of [(32766, 7), 229315, 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 (40, 47, 32766)-net over F2, using
(208−14, 208, 2828968)-Net over F2 — Digital
Digital (194, 208, 2828968)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 2828968, F2, 3, 14) (dual of [(2828968, 3), 8486696, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- linear OOA(2161, 2796201, F2, 3, 14) (dual of [(2796201, 3), 8388442, 15]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- (u, u+v)-construction [i] based on
(208−14, 208, large)-Net in Base 2 — Upper bound on s
There is no (194, 208, large)-net in base 2, because
- 12 times m-reduction [i] would yield (194, 196, large)-net in base 2, but