Best Known (48, 73, s)-Nets in Base 128
(48, 73, 174762)-Net over F128 — Constructive and digital
Digital (48, 73, 174762)-net over F128, using
- net defined by OOA [i] based on linear OOA(12873, 174762, F128, 25, 25) (dual of [(174762, 25), 4368977, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12873, 2097145, F128, 25) (dual of [2097145, 2097072, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(12873, 2097152, F128, 25) (dual of [2097152, 2097079, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12873, 2097145, F128, 25) (dual of [2097145, 2097072, 26]-code), using
(48, 73, 699051)-Net over F128 — Digital
Digital (48, 73, 699051)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12873, 699051, F128, 3, 25) (dual of [(699051, 3), 2097080, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12873, 2097153, F128, 25) (dual of [2097153, 2097080, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12873, 2097153, F128, 25) (dual of [2097153, 2097080, 26]-code), using
(48, 73, large)-Net in Base 128 — Upper bound on s
There is no (48, 73, large)-net in base 128, because
- 23 times m-reduction [i] would yield (48, 50, large)-net in base 128, but