Best Known (184, 209, s)-Nets in Base 3
(184, 209, 132860)-Net over F3 — Constructive and digital
Digital (184, 209, 132860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3209, 132860, F3, 25, 25) (dual of [(132860, 25), 3321291, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3209, 1594321, F3, 25) (dual of [1594321, 1594112, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3209, 1594323, F3, 25) (dual of [1594323, 1594114, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3209, 1594323, F3, 25) (dual of [1594323, 1594114, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3209, 1594321, F3, 25) (dual of [1594321, 1594112, 26]-code), using
(184, 209, 322659)-Net over F3 — Digital
Digital (184, 209, 322659)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3209, 322659, F3, 4, 25) (dual of [(322659, 4), 1290427, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 398581, F3, 4, 25) (dual of [(398581, 4), 1594115, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- OOA 4-folding [i] based on linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(3209, 398581, F3, 4, 25) (dual of [(398581, 4), 1594115, 26]-NRT-code), using
(184, 209, large)-Net in Base 3 — Upper bound on s
There is no (184, 209, large)-net in base 3, because
- 23 times m-reduction [i] would yield (184, 186, large)-net in base 3, but