Best Known (97−25, 97, s)-Nets in Base 32
(97−25, 97, 87381)-Net over F32 — Constructive and digital
Digital (72, 97, 87381)-net over F32, using
- net defined by OOA [i] based on linear OOA(3297, 87381, F32, 25, 25) (dual of [(87381, 25), 2184428, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3297, 1048573, F32, 25) (dual of [1048573, 1048476, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3297, 1048573, F32, 25) (dual of [1048573, 1048476, 26]-code), using
(97−25, 97, 582708)-Net over F32 — Digital
Digital (72, 97, 582708)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3297, 582708, F32, 25) (dual of [582708, 582611, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3297, 1048576, F32, 25) (dual of [1048576, 1048479, 26]-code), using
(97−25, 97, large)-Net in Base 32 — Upper bound on s
There is no (72, 97, large)-net in base 32, because
- 23 times m-reduction [i] would yield (72, 74, large)-net in base 32, but