Best Known (41, 41+8, s)-Nets in Base 8
(41, 41+8, 524287)-Net over F8 — Constructive and digital
Digital (41, 49, 524287)-net over F8, using
- net defined by OOA [i] based on linear OOA(849, 524287, F8, 8, 8) (dual of [(524287, 8), 4194247, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(849, 2097148, F8, 8) (dual of [2097148, 2097099, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(849, 2097151, F8, 8) (dual of [2097151, 2097102, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(849, 2097151, F8, 8) (dual of [2097151, 2097102, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(849, 2097148, F8, 8) (dual of [2097148, 2097099, 9]-code), using
(41, 41+8, 2097151)-Net over F8 — Digital
Digital (41, 49, 2097151)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(849, 2097151, F8, 8) (dual of [2097151, 2097102, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
(41, 41+8, large)-Net in Base 8 — Upper bound on s
There is no (41, 49, large)-net in base 8, because
- 6 times m-reduction [i] would yield (41, 43, large)-net in base 8, but