Best Known (199−3, 199, s)-Nets in Base 4
(199−3, 199, large)-Net over F4 — Constructive and digital
Digital (196, 199, large)-net over F4, using
- t-expansion [i] based on digital (195, 199, large)-net over F4, using
- 8 times m-reduction [i] based on digital (195, 207, large)-net over F4, using
- trace code for nets [i] based on digital (57, 69, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 2796201, F64, 15, 12) (dual of [(2796201, 15), 41942946, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6469, 5592403, F64, 3, 12) (dual of [(5592403, 3), 16777140, 13]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6466, 5592402, F64, 3, 12) (dual of [(5592402, 3), 16777140, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6421, 2796201, F64, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- linear OOA(6445, 2796201, F64, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- linear OOA(6421, 2796201, F64, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6466, 5592402, F64, 3, 12) (dual of [(5592402, 3), 16777140, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6469, 5592403, F64, 3, 12) (dual of [(5592403, 3), 16777140, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6469, 2796201, F64, 15, 12) (dual of [(2796201, 15), 41942946, 13]-NRT-code), using
- trace code for nets [i] based on digital (57, 69, 2796201)-net over F64, using
- 8 times m-reduction [i] based on digital (195, 207, large)-net over F4, using
(199−3, 199, large)-Net in Base 4 — Upper bound on s
There is no (196, 199, large)-net in base 4, because
- 1 times m-reduction [i] would yield (196, 198, large)-net in base 4, but