Best Known (194, 194+21, s)-Nets in Base 3
(194, 194+21, 838860)-Net over F3 — Constructive and digital
Digital (194, 215, 838860)-net over F3, using
- 35 times duplication [i] based on digital (189, 210, 838860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3210, 838860, F3, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3210, 8388601, F3, 21) (dual of [8388601, 8388391, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3210, 8388601, F3, 21) (dual of [8388601, 8388391, 22]-code), using
- net defined by OOA [i] based on linear OOA(3210, 838860, F3, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
(194, 194+21, 2796202)-Net over F3 — Digital
Digital (194, 215, 2796202)-net over F3, using
- 32 times duplication [i] based on digital (192, 213, 2796202)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3213, 2796202, F3, 3, 21) (dual of [(2796202, 3), 8388393, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3210, 2796201, F3, 3, 21) (dual of [(2796201, 3), 8388393, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- OOA 3-folding [i] based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3210, 2796201, F3, 3, 21) (dual of [(2796201, 3), 8388393, 22]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3213, 2796202, F3, 3, 21) (dual of [(2796202, 3), 8388393, 22]-NRT-code), using
(194, 194+21, large)-Net in Base 3 — Upper bound on s
There is no (194, 215, large)-net in base 3, because
- 19 times m-reduction [i] would yield (194, 196, large)-net in base 3, but