Best Known (126−24, 126, s)-Nets in Base 5
(126−24, 126, 1305)-Net over F5 — Constructive and digital
Digital (102, 126, 1305)-net over F5, using
- 52 times duplication [i] based on digital (100, 124, 1305)-net over F5, using
- net defined by OOA [i] based on linear OOA(5124, 1305, F5, 24, 24) (dual of [(1305, 24), 31196, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5124, 15660, F5, 24) (dual of [15660, 15536, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5124, 15664, F5, 24) (dual of [15664, 15540, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] 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]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5124, 15664, F5, 24) (dual of [15664, 15540, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5124, 15660, F5, 24) (dual of [15660, 15536, 25]-code), using
- net defined by OOA [i] based on linear OOA(5124, 1305, F5, 24, 24) (dual of [(1305, 24), 31196, 25]-NRT-code), using
(126−24, 126, 15916)-Net over F5 — Digital
Digital (102, 126, 15916)-net over F5, using
(126−24, 126, large)-Net in Base 5 — Upper bound on s
There is no (102, 126, large)-net in base 5, because
- 22 times m-reduction [i] would yield (102, 104, large)-net in base 5, but