Best Known (95, 106, s)-Nets in Base 8
(95, 106, 3387775)-Net over F8 — Constructive and digital
Digital (95, 106, 3387775)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (19, 24, 32335)-net over F8, using
- net defined by OOA [i] based on linear OOA(824, 32335, F8, 6, 5) (dual of [(32335, 6), 193986, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(824, 32336, F8, 2, 5) (dual of [(32336, 2), 64648, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(80, 4042, F8, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(80, s, F8, 2, 0) with arbitrarily large s, using
- linear OOA(80, 4042, F8, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
- linear OOA(80, 4042, F8, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code) (see above)
- linear OOA(81, 4042, F8, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 2, 1) with arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 2, 1) with arbitrarily large s, using
- linear OOA(81, 4042, F8, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
- linear OOA(81, 4042, F8, 2, 1) (dual of [(4042, 2), 8083, 2]-NRT-code) (see above)
- linear OOA(85, 4042, F8, 2, 2) (dual of [(4042, 2), 8079, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(85, 4681, F8, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
- appending kth column [i] based on linear OA(85, 4681, F8, 2) (dual of [4681, 4676, 3]-code), using
- Hamming code H(5,8) [i]
- appending kth column [i] based on linear OA(85, 4681, F8, 2) (dual of [4681, 4676, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(85, 4681, F8, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
- linear OOA(816, 4042, F8, 2, 5) (dual of [(4042, 2), 8068, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(82, 9, F8, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;16,8) [i]
- linear OOA(814, 4033, F8, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- trace code [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OOA 2-folding [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- linear OOA(82, 9, F8, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(80, 4042, F8, 2, 0) (dual of [(4042, 2), 8084, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(824, 32336, F8, 2, 5) (dual of [(32336, 2), 64648, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(824, 32335, F8, 6, 5) (dual of [(32335, 6), 193986, 6]-NRT-code), using
- digital (71, 82, 3355440)-net over F8, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- digital (19, 24, 32335)-net over F8, using
(95, 106, 3425401)-Net in Base 8 — Constructive
(95, 106, 3425401)-net in base 8, using
- (u, u+v)-construction [i] based on
- (19, 24, 69961)-net in base 8, using
- net defined by OOA [i] based on OOA(824, 69961, S8, 6, 5), using
- OOA stacking with additional row [i] based on OOA(824, 69962, S8, 2, 5), using
- (u, u+v)-construction [i] based on
- linear OOA(85, 4681, F8, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
- appending kth column [i] based on linear OA(85, 4681, F8, 2) (dual of [4681, 4676, 3]-code), using
- Hamming code H(5,8) [i]
- appending kth column [i] based on linear OA(85, 4681, F8, 2) (dual of [4681, 4676, 3]-code), using
- OOA(819, 65281, S8, 2, 5), using
- OOA 2-folding [i] based on OA(819, 130562, S8, 5), using
- discarding parts of the base [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- discarding parts of the base [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- OOA 2-folding [i] based on OA(819, 130562, S8, 5), using
- linear OOA(85, 4681, F8, 2, 2) (dual of [(4681, 2), 9357, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(824, 69962, S8, 2, 5), using
- net defined by OOA [i] based on OOA(824, 69961, S8, 6, 5), using
- digital (71, 82, 3355440)-net over F8, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6441, 8388601, F64, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(6441, 1677720, F64, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F64, using
- (19, 24, 69961)-net in base 8, using
(95, 106, large)-Net over F8 — Digital
Digital (95, 106, large)-net over F8, using
- 81 times duplication [i] based on digital (94, 105, large)-net over F8, using
- t-expansion [i] based on digital (90, 105, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- t-expansion [i] based on digital (90, 105, large)-net over F8, using
(95, 106, large)-Net in Base 8 — Upper bound on s
There is no (95, 106, large)-net in base 8, because
- 9 times m-reduction [i] would yield (95, 97, large)-net in base 8, but