Best Known (74, 74+28, s)-Nets in Base 32
(74, 74+28, 2417)-Net over F32 — Constructive and digital
Digital (74, 102, 2417)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (55, 83, 2341)-net over F32, using
- net defined by OOA [i] based on linear OOA(3283, 2341, F32, 28, 28) (dual of [(2341, 28), 65465, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 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
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
- net defined by OOA [i] based on linear OOA(3283, 2341, F32, 28, 28) (dual of [(2341, 28), 65465, 29]-NRT-code), using
- digital (5, 19, 76)-net over F32, using
(74, 74+28, 18725)-Net in Base 32 — Constructive
(74, 102, 18725)-net in base 32, using
- base change [i] based on digital (57, 85, 18725)-net over F64, using
- 1 times m-reduction [i] based on digital (57, 86, 18725)-net over F64, using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (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([0,14]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- 1 times m-reduction [i] based on digital (57, 86, 18725)-net over F64, using
(74, 74+28, 171081)-Net over F32 — Digital
Digital (74, 102, 171081)-net over F32, using
(74, 74+28, large)-Net in Base 32 — Upper bound on s
There is no (74, 102, large)-net in base 32, because
- 26 times m-reduction [i] would yield (74, 76, large)-net in base 32, but