Best Known (134, 134+14, s)-Nets in Base 9
(134, 134+14, 2751119)-Net over F9 — Constructive and digital
Digital (134, 148, 2751119)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (35, 42, 354377)-net over F9, using
- net defined by OOA [i] based on linear OOA(942, 354377, F9, 9, 7) (dual of [(354377, 9), 3189351, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(942, 354378, F9, 3, 7) (dual of [(354378, 3), 1063092, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(94, 82, F9, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
- linear OOA(938, 354296, F9, 3, 7) (dual of [(354296, 3), 1062850, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- OOA 3-folding [i] based on linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(942, 354378, F9, 3, 7) (dual of [(354378, 3), 1063092, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(942, 354377, F9, 9, 7) (dual of [(354377, 9), 3189351, 8]-NRT-code), using
- digital (92, 106, 2396742)-net over F9, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- digital (35, 42, 354377)-net over F9, using
(134, 134+14, large)-Net over F9 — Digital
Digital (134, 148, large)-net over F9, using
- 93 times duplication [i] based on digital (131, 145, large)-net over F9, using
- t-expansion [i] based on digital (124, 145, large)-net over F9, using
(134, 134+14, large)-Net in Base 9 — Upper bound on s
There is no (134, 148, large)-net in base 9, because
- 12 times m-reduction [i] would yield (134, 136, large)-net in base 9, but