Best Known (50, 67, s)-Nets in Base 128
(50, 67, 1048575)-Net over F128 — Constructive and digital
Digital (50, 67, 1048575)-net over F128, using
- 1282 times duplication [i] based on digital (48, 65, 1048575)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 1048575, F128, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12865, 8388601, F128, 17) (dual of [8388601, 8388536, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(12865, large, F128, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12865, large, F128, 17) (dual of [large, large−65, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12865, 8388601, F128, 17) (dual of [8388601, 8388536, 18]-code), using
- net defined by OOA [i] based on linear OOA(12865, 1048575, F128, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
(50, 67, 1048833)-Net in Base 128 — Constructive
(50, 67, 1048833)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 11, 258)-net in base 128, using
- 5 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- 5 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- (39, 56, 1048575)-net in base 128, using
- base change [i] based on digital (32, 49, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- base change [i] based on digital (32, 49, 1048575)-net over F256, using
- (3, 11, 258)-net in base 128, using
(50, 67, large)-Net over F128 — Digital
Digital (50, 67, large)-net over F128, using
- 1281 times duplication [i] based on digital (49, 66, large)-net over F128, using
- t-expansion [i] based on digital (48, 66, large)-net over F128, using
(50, 67, large)-Net in Base 128 — Upper bound on s
There is no (50, 67, large)-net in base 128, because
- 15 times m-reduction [i] would yield (50, 52, large)-net in base 128, but