Best Known (133, 133+19, s)-Nets in Base 8
(133, 133+19, 1864134)-Net over F8 — Constructive and digital
Digital (133, 152, 1864134)-net over F8, using
- 83 times duplication [i] based on digital (130, 149, 1864134)-net over F8, using
- net defined by OOA [i] based on linear OOA(8149, 1864134, F8, 21, 19) (dual of [(1864134, 21), 39146665, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8149, 5592403, F8, 3, 19) (dual of [(5592403, 3), 16777060, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8149, 5592403, F8, 3, 19) (dual of [(5592403, 3), 16777060, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8149, 1864134, F8, 21, 19) (dual of [(1864134, 21), 39146665, 20]-NRT-code), using
(133, 133+19, large)-Net over F8 — Digital
Digital (133, 152, large)-net over F8, using
- t-expansion [i] based on digital (131, 152, large)-net over F8, using
- 1 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
- 1 times m-reduction [i] based on digital (131, 153, large)-net over F8, using
(133, 133+19, large)-Net in Base 8 — Upper bound on s
There is no (133, 152, large)-net in base 8, because
- 17 times m-reduction [i] would yield (133, 135, large)-net in base 8, but