Best Known (225−21, 225, s)-Nets in Base 3
(225−21, 225, 838875)-Net over F3 — Constructive and digital
Digital (204, 225, 838875)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 15)-net over F3, using
- 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
(225−21, 225, 3076804)-Net over F3 — Digital
Digital (204, 225, 3076804)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3225, 3076804, F3, 2, 21) (dual of [(3076804, 2), 6153383, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3225, 4194316, F3, 2, 21) (dual of [(4194316, 2), 8388407, 22]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(315, 15, F3, 2, 10) (dual of [(15, 2), 15, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 15, 15)-net over F3, using
- linear OOA(3210, 4194301, F3, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 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 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
- linear OOA(315, 15, F3, 2, 10) (dual of [(15, 2), 15, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3225, 4194316, F3, 2, 21) (dual of [(4194316, 2), 8388407, 22]-NRT-code), using
(225−21, 225, large)-Net in Base 3 — Upper bound on s
There is no (204, 225, large)-net in base 3, because
- 19 times m-reduction [i] would yield (204, 206, large)-net in base 3, but