Best Known (122, 122+33, s)-Nets in Base 8
(122, 122+33, 2051)-Net over F8 — Constructive and digital
Digital (122, 155, 2051)-net over F8, using
- net defined by OOA [i] based on linear OOA(8155, 2051, F8, 33, 33) (dual of [(2051, 33), 67528, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8155, 32817, F8, 33) (dual of [32817, 32662, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8154, 32816, F8, 33) (dual of [32816, 32662, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(24) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(813, 48, F8, 7) (dual of [48, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(32) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8154, 32816, F8, 33) (dual of [32816, 32662, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8155, 32817, F8, 33) (dual of [32817, 32662, 34]-code), using
(122, 122+33, 43280)-Net over F8 — Digital
Digital (122, 155, 43280)-net over F8, using
(122, 122+33, large)-Net in Base 8 — Upper bound on s
There is no (122, 155, large)-net in base 8, because
- 31 times m-reduction [i] would yield (122, 124, large)-net in base 8, but