Best Known (120, 120+14, s)-Nets in Base 9
(120, 120+14, 2401119)-Net over F9 — Constructive and digital
Digital (120, 134, 2401119)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (21, 28, 4377)-net over F9, using
- net defined by OOA [i] based on linear OOA(928, 4377, F9, 7, 7) (dual of [(4377, 7), 30611, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(928, 13132, F9, 7) (dual of [13132, 13104, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(928, 13134, F9, 7) (dual of [13134, 13106, 8]-code), using
- trace code [i] based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- trace code [i] based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(928, 13134, F9, 7) (dual of [13134, 13106, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(928, 13132, F9, 7) (dual of [13132, 13104, 8]-code), using
- net defined by OOA [i] based on linear OOA(928, 4377, F9, 7, 7) (dual of [(4377, 7), 30611, 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 (21, 28, 4377)-net over F9, using
(120, 120+14, large)-Net over F9 — Digital
Digital (120, 134, large)-net over F9, using
- t-expansion [i] based on digital (117, 134, large)-net over F9, using
- 3 times m-reduction [i] based on digital (117, 137, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9137, large, F9, 20) (dual of [large, large−137, 21]-code), using
- 3 times m-reduction [i] based on digital (117, 137, large)-net over F9, using
(120, 120+14, large)-Net in Base 9 — Upper bound on s
There is no (120, 134, large)-net in base 9, because
- 12 times m-reduction [i] would yield (120, 122, large)-net in base 9, but