Best Known (48, 48+10, s)-Nets in Base 32
(48, 48+10, 1679705)-Net over F32 — Constructive and digital
Digital (48, 58, 1679705)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 1985)-net over F32, using
- net defined by OOA [i] based on linear OOA(3212, 1985, F32, 5, 5) (dual of [(1985, 5), 9913, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3212, 3971, F32, 5) (dual of [3971, 3959, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3212, 3972, F32, 5) (dual of [3972, 3960, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code) (see above)
- linear OA(323, 993, F32, 2) (dual of [993, 990, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(3212, 3972, F32, 5) (dual of [3972, 3960, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3212, 3971, F32, 5) (dual of [3971, 3959, 6]-code), using
- net defined by OOA [i] based on linear OOA(3212, 1985, F32, 5, 5) (dual of [(1985, 5), 9913, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (7, 12, 1985)-net over F32, using
(48, 48+10, 1710360)-Net in Base 32 — Constructive
(48, 58, 1710360)-net in base 32, using
- 322 times duplication [i] based on (46, 56, 1710360)-net in base 32, using
- base change [i] based on digital (25, 35, 1710360)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- digital (18, 28, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25628, 8388600, F256, 10) (dual of [8388600, 8388572, 11]-code), using
- net defined by OOA [i] based on linear OOA(25628, 1677720, F256, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
- digital (2, 7, 32640)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (25, 35, 1710360)-net over F256, using
(48, 48+10, large)-Net over F32 — Digital
Digital (48, 58, large)-net over F32, using
- 3 times m-reduction [i] based on digital (48, 61, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
(48, 48+10, large)-Net in Base 32 — Upper bound on s
There is no (48, 58, large)-net in base 32, because
- 8 times m-reduction [i] would yield (48, 50, large)-net in base 32, but