Best Known (87, 97, s)-Nets in Base 8
(87, 97, 3387704)-Net over F8 — Constructive and digital
Digital (87, 97, 3387704)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (18, 23, 32264)-net over F8, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 4033)-net over F8, using
- s-reduction based on digital (0, 0, s)-net over F8 with arbitrarily large s, using
- digital (0, 0, 4033)-net over F8 (see above)
- digital (0, 0, 4033)-net over F8 (see above)
- digital (0, 1, 4033)-net over F8, using
- s-reduction based on digital (0, 1, s)-net over F8 with arbitrarily large s, using
- digital (0, 1, 4033)-net over F8 (see above)
- digital (0, 1, 4033)-net over F8 (see above)
- digital (3, 5, 4033)-net over F8, using
- s-reduction based on digital (3, 5, 4681)-net over F8, using
- digital (10, 15, 4033)-net over F8, using
- net defined by OOA [i] based on linear OOA(815, 4033, F8, 5, 5) (dual of [(4033, 5), 20150, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(815, 8067, F8, 5) (dual of [8067, 8052, 6]-code), using
- 1 times code embedding in larger space [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
- 1 times code embedding in larger space [i] based on linear OA(814, 8066, F8, 5) (dual of [8066, 8052, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(815, 8067, F8, 5) (dual of [8067, 8052, 6]-code), using
- net defined by OOA [i] based on linear OOA(815, 4033, F8, 5, 5) (dual of [(4033, 5), 20150, 6]-NRT-code), using
- digital (0, 0, 4033)-net over F8, using
- generalized (u, u+v)-construction [i] based on
- digital (64, 74, 3355440)-net over F8, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- digital (18, 23, 32264)-net over F8, using
(87, 97, 3421305)-Net in Base 8 — Constructive
(87, 97, 3421305)-net in base 8, using
- (u, u+v)-construction [i] based on
- (18, 23, 65865)-net in base 8, using
- net defined by OOA [i] based on OOA(823, 65865, S8, 6, 5), using
- OOA stacking with additional row [i] based on OOA(823, 65866, S8, 2, 5), using
- (u, u+v)-construction [i] based on
- linear OOA(84, 585, F8, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
- appending kth column [i] based on linear OA(84, 585, F8, 2) (dual of [585, 581, 3]-code), using
- Hamming code H(4,8) [i]
- appending kth column [i] based on linear OA(84, 585, F8, 2) (dual of [585, 581, 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(84, 585, F8, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(823, 65866, S8, 2, 5), using
- net defined by OOA [i] based on OOA(823, 65865, S8, 6, 5), using
- digital (64, 74, 3355440)-net over F8, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- (18, 23, 65865)-net in base 8, using
(87, 97, large)-Net over F8 — Digital
Digital (87, 97, large)-net over F8, using
- t-expansion [i] based on digital (83, 97, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
(87, 97, large)-Net in Base 8 — Upper bound on s
There is no (87, 97, large)-net in base 8, because
- 8 times m-reduction [i] would yield (87, 89, large)-net in base 8, but