Best Known (79, 106, s)-Nets in Base 32
(79, 106, 80660)-Net over F32 — Constructive and digital
Digital (79, 106, 80660)-net over F32, using
- net defined by OOA [i] based on linear OOA(32106, 80660, F32, 27, 27) (dual of [(80660, 27), 2177714, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(32106, 1048581, F32, 27) (dual of [1048581, 1048475, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(32106, 1048586, F32, 27) (dual of [1048586, 1048480, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(32105, 1048577, F32, 27) (dual of [1048577, 1048472, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,13]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(32106, 1048586, F32, 27) (dual of [1048586, 1048480, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(32106, 1048581, F32, 27) (dual of [1048581, 1048475, 28]-code), using
(79, 106, 688472)-Net over F32 — Digital
Digital (79, 106, 688472)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32106, 688472, F32, 27) (dual of [688472, 688366, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(32106, 1048586, F32, 27) (dual of [1048586, 1048480, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(32105, 1048577, F32, 27) (dual of [1048577, 1048472, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,13]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(32106, 1048586, F32, 27) (dual of [1048586, 1048480, 28]-code), using
(79, 106, large)-Net in Base 32 — Upper bound on s
There is no (79, 106, large)-net in base 32, because
- 25 times m-reduction [i] would yield (79, 81, large)-net in base 32, but