Best Known (66, 66+8, s)-Nets in Base 8
(66, 66+8, 4210686)-Net over F8 — Constructive and digital
Digital (66, 74, 4210686)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (12, 16, 16386)-net over F8, using
- net defined by OOA [i] based on linear OOA(816, 16386, F8, 4, 4) (dual of [(16386, 4), 65528, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(816, 16386, F8, 3, 4) (dual of [(16386, 3), 49142, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(816, 32772, F8, 4) (dual of [32772, 32756, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(816, 32773, F8, 4) (dual of [32773, 32757, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(816, 32768, F8, 4) (dual of [32768, 32752, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(811, 32768, F8, 3) (dual of [32768, 32757, 4]-code or 32768-cap in PG(10,8)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(816, 32773, F8, 4) (dual of [32773, 32757, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(816, 32772, F8, 4) (dual of [32772, 32756, 5]-code), using
- appending kth column [i] based on linear OOA(816, 16386, F8, 3, 4) (dual of [(16386, 3), 49142, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(816, 16386, F8, 4, 4) (dual of [(16386, 4), 65528, 5]-NRT-code), using
- digital (50, 58, 4194300)-net over F8, using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- digital (12, 16, 16386)-net over F8, using
(66, 66+8, 4259580)-Net in Base 8 — Constructive
(66, 74, 4259580)-net in base 8, using
- (u, u+v)-construction [i] based on
- (12, 16, 65280)-net in base 8, using
- base change [i] based on digital (8, 12, 65280)-net over F16, using
- net defined by OOA [i] based on linear OOA(1612, 65280, F16, 4, 4) (dual of [(65280, 4), 261108, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- net defined by OOA [i] based on linear OOA(1612, 65280, F16, 4, 4) (dual of [(65280, 4), 261108, 5]-NRT-code), using
- base change [i] based on digital (8, 12, 65280)-net over F16, using
- digital (50, 58, 4194300)-net over F8, using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- trace code [i] based on linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(858, 8388602, F8, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(858, 8388601, F8, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(858, 4194300, F8, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
- (12, 16, 65280)-net in base 8, using
(66, 66+8, large)-Net over F8 — Digital
Digital (66, 74, large)-net over F8, using
- 81 times duplication [i] based on digital (65, 73, large)-net over F8, using
- t-expansion [i] based on digital (62, 73, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
- t-expansion [i] based on digital (62, 73, large)-net over F8, using
(66, 66+8, large)-Net in Base 8 — Upper bound on s
There is no (66, 74, large)-net in base 8, because
- 6 times m-reduction [i] would yield (66, 68, large)-net in base 8, but