Best Known (168, 168+25, s)-Nets in Base 3
(168, 168+25, 44286)-Net over F3 — Constructive and digital
Digital (168, 193, 44286)-net over F3, using
- net defined by OOA [i] based on linear OOA(3193, 44286, F3, 25, 25) (dual of [(44286, 25), 1106957, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3193, 531433, F3, 25) (dual of [531433, 531240, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3193, 531433, F3, 25) (dual of [531433, 531240, 26]-code), using
(168, 168+25, 132860)-Net over F3 — Digital
Digital (168, 193, 132860)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3193, 132860, F3, 4, 25) (dual of [(132860, 4), 531247, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3193, 531440, F3, 25) (dual of [531440, 531247, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using
- OOA 4-folding [i] based on linear OA(3193, 531440, F3, 25) (dual of [531440, 531247, 26]-code), using
(168, 168+25, large)-Net in Base 3 — Upper bound on s
There is no (168, 193, large)-net in base 3, because
- 23 times m-reduction [i] would yield (168, 170, large)-net in base 3, but