Best Known (79, 79+17, s)-Nets in Base 32
(79, 79+17, 1048831)-Net over F32 — Constructive and digital
Digital (79, 96, 1048831)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 15, 256)-net over F32, using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using
- net defined by OOA [i] based on linear OOA(3215, 256, F32, 8, 8) (dual of [(256, 8), 2033, 9]-NRT-code), using
- digital (64, 81, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- digital (7, 15, 256)-net over F32, using
(79, 79+17, 1049599)-Net in Base 32 — Constructive
(79, 96, 1049599)-net in base 32, using
- base change [i] based on digital (63, 80, 1049599)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (7, 15, 1024)-net over F64, using
- net defined by OOA [i] based on linear OOA(6415, 1024, F64, 8, 8) (dual of [(1024, 8), 8177, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using
- net defined by OOA [i] based on linear OOA(6415, 1024, F64, 8, 8) (dual of [(1024, 8), 8177, 9]-NRT-code), using
- digital (48, 65, 1048575)-net over F64, using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- digital (7, 15, 1024)-net over F64, using
- (u, u+v)-construction [i] based on
(79, 79+17, large)-Net over F32 — Digital
Digital (79, 96, large)-net over F32, using
- 4 times m-reduction [i] based on digital (79, 100, large)-net over F32, using
(79, 79+17, large)-Net in Base 32 — Upper bound on s
There is no (79, 96, large)-net in base 32, because
- 15 times m-reduction [i] would yield (79, 81, large)-net in base 32, but