Best Known (74, 74+13, s)-Nets in Base 32
(74, 74+13, 2796200)-Net over F32 — Constructive and digital
Digital (74, 87, 2796200)-net over F32, using
- net defined by OOA [i] based on linear OOA(3287, 2796200, F32, 14, 13) (dual of [(2796200, 14), 39146713, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3287, 8388601, F32, 2, 13) (dual of [(8388601, 2), 16777115, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3287, 8388602, F32, 2, 13) (dual of [(8388602, 2), 16777117, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3226, 4194301, F32, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3226, 8388602, F32, 6) (dual of [8388602, 8388576, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- OOA 2-folding [i] based on linear OA(3226, 8388602, F32, 6) (dual of [8388602, 8388576, 7]-code), using
- linear OOA(3261, 4194301, F32, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- linear OOA(3226, 4194301, F32, 2, 6) (dual of [(4194301, 2), 8388576, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3287, 8388602, F32, 2, 13) (dual of [(8388602, 2), 16777117, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3287, 8388601, F32, 2, 13) (dual of [(8388601, 2), 16777115, 14]-NRT-code), using
(74, 74+13, large)-Net over F32 — Digital
Digital (74, 87, large)-net over F32, using
- t-expansion [i] based on digital (72, 87, large)-net over F32, using
- 4 times m-reduction [i] based on digital (72, 91, large)-net over F32, using
(74, 74+13, large)-Net in Base 32 — Upper bound on s
There is no (74, 87, large)-net in base 32, because
- 11 times m-reduction [i] would yield (74, 76, large)-net in base 32, but