Best Known (35, 35+14, s)-Nets in Base 8
(35, 35+14, 585)-Net over F8 — Constructive and digital
Digital (35, 49, 585)-net over F8, using
- net defined by OOA [i] based on linear OOA(849, 585, F8, 14, 14) (dual of [(585, 14), 8141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(849, 4095, F8, 14) (dual of [4095, 4046, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(849, 4095, F8, 14) (dual of [4095, 4046, 15]-code), using
(35, 35+14, 3088)-Net over F8 — Digital
Digital (35, 49, 3088)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(849, 3088, F8, 14) (dual of [3088, 3039, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(849, 4096, F8, 14) (dual of [4096, 4047, 15]-code), using
(35, 35+14, 1012625)-Net in Base 8 — Upper bound on s
There is no (35, 49, 1012626)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 178 406745 407834 065870 690512 316548 973705 857352 > 849 [i]