Best Known (219−6, 219, s)-Nets in Base 4
(219−6, 219, large)-Net over F4 — Constructive and digital
Digital (213, 219, large)-net over F4, using
- t-expansion [i] based on digital (206, 219, large)-net over F4, using
- trace code for nets [i] based on digital (60, 73, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6473, 2796201, F64, 15, 13) (dual of [(2796201, 15), 41942942, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6473, 5592403, F64, 3, 13) (dual of [(5592403, 3), 16777136, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(6470, 5592402, F64, 3, 13) (dual of [(5592402, 3), 16777136, 14]-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(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-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(6470, 5592402, F64, 3, 13) (dual of [(5592402, 3), 16777136, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6473, 5592403, F64, 3, 13) (dual of [(5592403, 3), 16777136, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6473, 2796201, F64, 15, 13) (dual of [(2796201, 15), 41942942, 14]-NRT-code), using
- trace code for nets [i] based on digital (60, 73, 2796201)-net over F64, using
(219−6, 219, large)-Net in Base 4 — Upper bound on s
There is no (213, 219, large)-net in base 4, because
- 4 times m-reduction [i] would yield (213, 215, large)-net in base 4, but