Best Known (163−9, 163, s)-Nets in Base 2
(163−9, 163, 8388602)-Net over F2 — Constructive and digital
Digital (154, 163, 8388602)-net over F2, using
- 23 times duplication [i] based on digital (151, 160, 8388602)-net over F2, using
- net defined by OOA [i] based on linear OOA(2160, 8388602, F2, 9, 9) (dual of [(8388602, 9), 75497258, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2160, 8388602, F2, 8, 9) (dual of [(8388602, 8), 67108656, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(244, 4194305, F2, 8, 4) (dual of [(4194305, 8), 33554396, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(244, 4194305, F2, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(244, 4194305, F2, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (40, 44, 4194305)-net over F2, using
- appending kth column [i] based on linear OOA(244, 4194305, F2, 3, 4) (dual of [(4194305, 3), 12582871, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(244, 4194305, F2, 4, 4) (dual of [(4194305, 4), 16777176, 5]-NRT-code), using
- linear OOA(2116, 4194301, F2, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2116, large, F2, 2, 9), using
- linear OOA(244, 4194305, F2, 8, 4) (dual of [(4194305, 8), 33554396, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2160, 8388602, F2, 8, 9) (dual of [(8388602, 8), 67108656, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2160, 8388602, F2, 9, 9) (dual of [(8388602, 9), 75497258, 10]-NRT-code), using
(163−9, 163, large)-Net over F2 — Digital
Digital (154, 163, large)-net over F2, using
- 211 times duplication [i] based on digital (143, 152, large)-net over F2, using
- t-expansion [i] based on digital (141, 152, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- t-expansion [i] based on digital (141, 152, large)-net over F2, using
(163−9, 163, large)-Net in Base 2 — Upper bound on s
There is no (154, 163, large)-net in base 2, because
- 7 times m-reduction [i] would yield (154, 156, large)-net in base 2, but