Best Known (96, 121, s)-Nets in Base 5
(96, 121, 1302)-Net over F5 — Constructive and digital
Digital (96, 121, 1302)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 1302, F5, 25, 25) (dual of [(1302, 25), 32429, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5121, 15625, F5, 25) (dual of [15625, 15504, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5121, 15625, F5, 25) (dual of [15625, 15504, 26]-code), using
(96, 121, 10436)-Net over F5 — Digital
Digital (96, 121, 10436)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5121, 10436, F5, 25) (dual of [10436, 10315, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using
(96, 121, large)-Net in Base 5 — Upper bound on s
There is no (96, 121, large)-net in base 5, because
- 23 times m-reduction [i] would yield (96, 98, large)-net in base 5, but