Best Known (10, 10+5, s)-Nets in Base 32
(10, 10+5, 16928)-Net over F32 — Constructive and digital
Digital (10, 15, 16928)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 529)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 with arbitrarily large s, using
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 0, 529)-net over F32 (see above)
- digital (0, 1, 529)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 529)-net over F32 (see above)
- digital (0, 1, 529)-net over F32 (see above)
- digital (1, 3, 529)-net over F32, using
- s-reduction based on digital (1, 3, 1057)-net over F32, using
- digital (4, 9, 529)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (2, 7, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- digital (0, 0, 529)-net over F32, using
(10, 10+5, 32864)-Net over F32 — Digital
Digital (10, 15, 32864)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3215, 32864, F32, 5) (dual of [32864, 32849, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
- linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 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, 1027, F32, 1) (dual of [1027, 1026, 2]-code) (see above)
- linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code) (see above)
- linear OA(323, 1027, F32, 2) (dual of [1027, 1024, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- Hamming code H(3,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 1057, F32, 2) (dual of [1057, 1054, 3]-code), using
- linear OA(329, 1027, F32, 5) (dual of [1027, 1018, 6]-code), using
- construction XX applied to C1 = C([1022,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([1022,3]) [i] based on
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(325, 1023, F32, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s (see above)
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([1022,3]) [i] based on
- linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code), using
- generalized (u, u+v)-construction [i] based on
(10, 10+5, 33697)-Net in Base 32 — Constructive
(10, 15, 33697)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (1, 3, 1057)-net over F32, using
- (7, 12, 32640)-net in base 32, using
- net defined by OOA [i] based on OOA(3212, 32640, S32, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(3212, 65281, S32, 5), using
- discarding parts of the base [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(3212, 65281, S32, 5), using
- net defined by OOA [i] based on OOA(3212, 32640, S32, 5, 5), using
(10, 10+5, large)-Net in Base 32 — Upper bound on s
There is no (10, 15, large)-net in base 32, because
- 3 times m-reduction [i] would yield (10, 12, large)-net in base 32, but