Best Known (61, 82, s)-Nets in Base 32
(61, 82, 104858)-Net over F32 — Constructive and digital
Digital (61, 82, 104858)-net over F32, using
- net defined by OOA [i] based on linear OOA(3282, 104858, F32, 21, 21) (dual of [(104858, 21), 2201936, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3282, 1048581, F32, 21) (dual of [1048581, 1048499, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3282, 1048586, F32, 21) (dual of [1048586, 1048504, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3281, 1048577, F32, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3273, 1048577, F32, 19) (dual of [1048577, 1048504, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3282, 1048586, F32, 21) (dual of [1048586, 1048504, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3282, 1048581, F32, 21) (dual of [1048581, 1048499, 22]-code), using
(61, 82, 667636)-Net over F32 — Digital
Digital (61, 82, 667636)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3282, 667636, F32, 21) (dual of [667636, 667554, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3282, 1048586, F32, 21) (dual of [1048586, 1048504, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3281, 1048577, F32, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3273, 1048577, F32, 19) (dual of [1048577, 1048504, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3282, 1048586, F32, 21) (dual of [1048586, 1048504, 22]-code), using
(61, 82, large)-Net in Base 32 — Upper bound on s
There is no (61, 82, large)-net in base 32, because
- 19 times m-reduction [i] would yield (61, 63, large)-net in base 32, but