Best Known (193, 193+16, s)-Nets in Base 2
(193, 193+16, 1048619)-Net over F2 — Constructive and digital
Digital (193, 209, 1048619)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (17, 25, 44)-net over F2, using
- digital (168, 184, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
(193, 193+16, 2000393)-Net over F2 — Digital
Digital (193, 209, 2000393)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2209, 2000393, F2, 4, 16) (dual of [(2000393, 4), 8001363, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 2097172, F2, 4, 16) (dual of [(2097172, 4), 8388479, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2209, 4194344, F2, 2, 16) (dual of [(4194344, 2), 8388479, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 4194345, F2, 2, 16) (dual of [(4194345, 2), 8388481, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(225, 44, F2, 2, 8) (dual of [(44, 2), 63, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (17, 25, 44)-net over F2, using
- linear OOA(2184, 4194301, F2, 2, 16) (dual of [(4194301, 2), 8388418, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2184, 8388602, F2, 16) (dual of [8388602, 8388418, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 2-folding [i] based on linear OA(2184, 8388602, F2, 16) (dual of [8388602, 8388418, 17]-code), using
- linear OOA(225, 44, F2, 2, 8) (dual of [(44, 2), 63, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2209, 4194345, F2, 2, 16) (dual of [(4194345, 2), 8388481, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2209, 4194344, F2, 2, 16) (dual of [(4194344, 2), 8388479, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2209, 2097172, F2, 4, 16) (dual of [(2097172, 4), 8388479, 17]-NRT-code), using
(193, 193+16, large)-Net in Base 2 — Upper bound on s
There is no (193, 209, large)-net in base 2, because
- 14 times m-reduction [i] would yield (193, 195, large)-net in base 2, but