Best Known (135, 149, s)-Nets in Base 8
(135, 149, 3095794)-Net over F8 — Constructive and digital
Digital (135, 149, 3095794)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (36, 43, 699052)-net over F8, using
- net defined by OOA [i] based on linear OOA(843, 699052, F8, 7, 7) (dual of [(699052, 7), 4893321, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(843, 2097157, F8, 7) (dual of [2097157, 2097114, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(843, 2097159, F8, 7) (dual of [2097159, 2097116, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(843, 2097152, F8, 7) (dual of [2097152, 2097109, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 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(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(843, 2097159, F8, 7) (dual of [2097159, 2097116, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(843, 2097157, F8, 7) (dual of [2097157, 2097114, 8]-code), using
- net defined by OOA [i] based on linear OOA(843, 699052, F8, 7, 7) (dual of [(699052, 7), 4893321, 8]-NRT-code), using
- digital (92, 106, 2396742)-net over F8, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F64, using
- digital (36, 43, 699052)-net over F8, using
(135, 149, large)-Net over F8 — Digital
Digital (135, 149, large)-net over F8, using
- t-expansion [i] based on digital (131, 149, large)-net over F8, using
- 4 times m-reduction [i] based on digital (131, 153, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8153, large, F8, 22) (dual of [large, large−153, 23]-code), using
- 4 times m-reduction [i] based on digital (131, 153, large)-net over F8, using
(135, 149, large)-Net in Base 8 — Upper bound on s
There is no (135, 149, large)-net in base 8, because
- 12 times m-reduction [i] would yield (135, 137, large)-net in base 8, but