Best Known (169−22, 169, s)-Nets in Base 3
(169−22, 169, 48312)-Net over F3 — Constructive and digital
Digital (147, 169, 48312)-net over F3, using
- net defined by OOA [i] based on linear OOA(3169, 48312, F3, 22, 22) (dual of [(48312, 22), 1062695, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3169, 531432, F3, 22) (dual of [531432, 531263, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3169, 531432, F3, 22) (dual of [531432, 531263, 23]-code), using
(169−22, 169, 132860)-Net over F3 — Digital
Digital (147, 169, 132860)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3169, 132860, F3, 4, 22) (dual of [(132860, 4), 531271, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3169, 531440, F3, 22) (dual of [531440, 531271, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using
- OOA 4-folding [i] based on linear OA(3169, 531440, F3, 22) (dual of [531440, 531271, 23]-code), using
(169−22, 169, large)-Net in Base 3 — Upper bound on s
There is no (147, 169, large)-net in base 3, because
- 20 times m-reduction [i] would yield (147, 149, large)-net in base 3, but