Best Known (32−8, 32, s)-Nets in Base 128
(32−8, 32, 2097150)-Net over F128 — Constructive and digital
Digital (24, 32, 2097150)-net over F128, using
- 1 times m-reduction [i] based on digital (24, 33, 2097150)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 2097150, F128, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12833, 8388601, F128, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(12833, large, F128, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12833, large, F128, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12833, 8388601, F128, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(12833, 2097150, F128, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
(32−8, 32, 2129790)-Net in Base 128 — Constructive
(24, 32, 2129790)-net in base 128, using
- base change [i] based on digital (20, 28, 2129790)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 6, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- net defined by OOA [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- digital (14, 22, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(25622, 8388600, F256, 8) (dual of [8388600, 8388578, 9]-code), using
- net defined by OOA [i] based on linear OOA(25622, 2097150, F256, 8, 8) (dual of [(2097150, 8), 16777178, 9]-NRT-code), using
- digital (2, 6, 32640)-net over F256, using
- (u, u+v)-construction [i] based on
(32−8, 32, large)-Net over F128 — Digital
Digital (24, 32, large)-net over F128, using
- 1 times m-reduction [i] based on digital (24, 33, large)-net over F128, using
(32−8, 32, large)-Net in Base 128 — Upper bound on s
There is no (24, 32, large)-net in base 128, because
- 6 times m-reduction [i] would yield (24, 26, large)-net in base 128, but