Best Known (213, 232, s)-Nets in Base 2
(213, 232, 932096)-Net over F2 — Constructive and digital
Digital (213, 232, 932096)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (12, 21, 29)-net over F2, using
- digital (192, 211, 932067)-net over F2, using
- net defined by OOA [i] based on linear OOA(2211, 932067, F2, 21, 19) (dual of [(932067, 21), 19573196, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2211, 932067, F2, 21, 19) (dual of [(932067, 21), 19573196, 20]-NRT-code), using
(213, 232, 1398130)-Net over F2 — Digital
Digital (213, 232, 1398130)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2232, 1398130, F2, 6, 19) (dual of [(1398130, 6), 8388548, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 29, F2, 6, 9) (dual of [(29, 6), 153, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 21, 29)-net over F2, using
- linear OOA(2211, 1398101, F2, 6, 19) (dual of [(1398101, 6), 8388395, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- linear OOA(221, 29, F2, 6, 9) (dual of [(29, 6), 153, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(213, 232, large)-Net in Base 2 — Upper bound on s
There is no (213, 232, large)-net in base 2, because
- 17 times m-reduction [i] would yield (213, 215, large)-net in base 2, but