Best Known (91, 91+24, s)-Nets in Base 5
(91, 91+24, 1302)-Net over F5 — Constructive and digital
Digital (91, 115, 1302)-net over F5, using
- net defined by OOA [i] based on linear OOA(5115, 1302, F5, 24, 24) (dual of [(1302, 24), 31133, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5115, 15624, F5, 24) (dual of [15624, 15509, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5115, 15624, F5, 24) (dual of [15624, 15509, 25]-code), using
(91, 91+24, 9463)-Net over F5 — Digital
Digital (91, 115, 9463)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5115, 9463, F5, 24) (dual of [9463, 9348, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
(91, 91+24, 6603336)-Net in Base 5 — Upper bound on s
There is no (91, 115, 6603337)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 240 741622 926948 781113 953923 572378 562850 789489 206281 283457 895502 348603 016602 941265 > 5115 [i]