Best Known (228−23, 228, s)-Nets in Base 3
(228−23, 228, 762600)-Net over F3 — Constructive and digital
Digital (205, 228, 762600)-net over F3, using
- 32 times duplication [i] based on digital (203, 226, 762600)-net over F3, using
- net defined by OOA [i] based on linear OOA(3226, 762600, F3, 23, 23) (dual of [(762600, 23), 17539574, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3226, 8388601, F3, 23) (dual of [8388601, 8388375, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3226, 8388601, F3, 23) (dual of [8388601, 8388375, 24]-code), using
- net defined by OOA [i] based on linear OOA(3226, 762600, F3, 23, 23) (dual of [(762600, 23), 17539574, 24]-NRT-code), using
(228−23, 228, 2097151)-Net over F3 — Digital
Digital (205, 228, 2097151)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3228, 2097151, F3, 4, 23) (dual of [(2097151, 4), 8388376, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3228, 4194302, F3, 2, 23) (dual of [(4194302, 2), 8388376, 24]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3226, 4194301, F3, 2, 23) (dual of [(4194301, 2), 8388376, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3226, 8388602, F3, 23) (dual of [8388602, 8388376, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3226, large, F3, 23) (dual of [large, large−226, 24]-code), using
- OOA 2-folding [i] based on linear OA(3226, 8388602, F3, 23) (dual of [8388602, 8388376, 24]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3226, 4194301, F3, 2, 23) (dual of [(4194301, 2), 8388376, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3228, 4194302, F3, 2, 23) (dual of [(4194302, 2), 8388376, 24]-NRT-code), using
(228−23, 228, large)-Net in Base 3 — Upper bound on s
There is no (205, 228, large)-net in base 3, because
- 21 times m-reduction [i] would yield (205, 207, large)-net in base 3, but