Best Known (45, 45+17, s)-Nets in Base 32
(45, 45+17, 4173)-Net over F32 — Constructive and digital
Digital (45, 62, 4173)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (1, 9, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (32, 49, 4096)-net over F32, using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using
- net defined by OOA [i] based on linear OOA(3249, 4096, F32, 17, 17) (dual of [(4096, 17), 69583, 18]-NRT-code), using
- digital (5, 13, 77)-net over F32, using
(45, 45+17, 32769)-Net in Base 32 — Constructive
(45, 62, 32769)-net in base 32, using
- 321 times duplication [i] based on (44, 61, 32769)-net in base 32, using
- net defined by OOA [i] based on OOA(3261, 32769, S32, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3261, 262153, S32, 17), using
- 1 times code embedding in larger space [i] based on OA(3260, 262152, S32, 17), using
- discarding parts of the base [i] based on linear OA(6450, 262152, F64, 17) (dual of [262152, 262102, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(6449, 262145, F64, 17) (dual of [262145, 262096, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- discarding parts of the base [i] based on linear OA(6450, 262152, F64, 17) (dual of [262152, 262102, 18]-code), using
- 1 times code embedding in larger space [i] based on OA(3260, 262152, S32, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(3261, 262153, S32, 17), using
- net defined by OOA [i] based on OOA(3261, 32769, S32, 17, 17), using
(45, 45+17, 149161)-Net over F32 — Digital
Digital (45, 62, 149161)-net over F32, using
(45, 45+17, large)-Net in Base 32 — Upper bound on s
There is no (45, 62, large)-net in base 32, because
- 15 times m-reduction [i] would yield (45, 47, large)-net in base 32, but