Best Known (74, 104, s)-Nets in Base 32
(74, 104, 2228)-Net over F32 — Constructive and digital
Digital (74, 104, 2228)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 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 (58, 88, 2184)-net over F32, using
- net defined by OOA [i] based on linear OOA(3288, 2184, F32, 30, 30) (dual of [(2184, 30), 65432, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3288, 32760, F32, 30) (dual of [32760, 32672, 31]-code), using
- net defined by OOA [i] based on linear OOA(3288, 2184, F32, 30, 30) (dual of [(2184, 30), 65432, 31]-NRT-code), using
- digital (1, 16, 44)-net over F32, using
(74, 104, 4370)-Net in Base 32 — Constructive
(74, 104, 4370)-net in base 32, using
- base change [i] based on digital (35, 65, 4370)-net over F256, using
- 1 times m-reduction [i] based on digital (35, 66, 4370)-net over F256, using
- net defined by OOA [i] based on linear OOA(25666, 4370, F256, 31, 31) (dual of [(4370, 31), 135404, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25666, 65551, F256, 31) (dual of [65551, 65485, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(25666, 65554, F256, 31) (dual of [65554, 65488, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25666, 65554, F256, 31) (dual of [65554, 65488, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25666, 65551, F256, 31) (dual of [65551, 65485, 32]-code), using
- net defined by OOA [i] based on linear OOA(25666, 4370, F256, 31, 31) (dual of [(4370, 31), 135404, 32]-NRT-code), using
- 1 times m-reduction [i] based on digital (35, 66, 4370)-net over F256, using
(74, 104, 94104)-Net over F32 — Digital
Digital (74, 104, 94104)-net over F32, using
(74, 104, large)-Net in Base 32 — Upper bound on s
There is no (74, 104, large)-net in base 32, because
- 28 times m-reduction [i] would yield (74, 76, large)-net in base 32, but