Best Known (123−26, 123, s)-Nets in Base 8
(123−26, 123, 2523)-Net over F8 — Constructive and digital
Digital (97, 123, 2523)-net over F8, using
- t-expansion [i] based on digital (96, 123, 2523)-net over F8, using
- net defined by OOA [i] based on linear OOA(8123, 2523, F8, 27, 27) (dual of [(2523, 27), 67998, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(891, 32768, F8, 21) (dual of [32768, 32677, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(8123, 32800, F8, 27) (dual of [32800, 32677, 28]-code), using
- net defined by OOA [i] based on linear OOA(8123, 2523, F8, 27, 27) (dual of [(2523, 27), 67998, 28]-NRT-code), using
(123−26, 123, 40352)-Net over F8 — Digital
Digital (97, 123, 40352)-net over F8, using
(123−26, 123, large)-Net in Base 8 — Upper bound on s
There is no (97, 123, large)-net in base 8, because
- 24 times m-reduction [i] would yield (97, 99, large)-net in base 8, but