Best Known (13, 18, s)-Nets in Base 32
(13, 18, 524293)-Net over F32 — Constructive and digital
Digital (13, 18, 524293)-net over F32, using
- net defined by OOA [i] based on linear OOA(3218, 524293, F32, 5, 5) (dual of [(524293, 5), 2621447, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3218, 1048587, F32, 5) (dual of [1048587, 1048569, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(3217, 1048577, F32, 5) (dual of [1048577, 1048560, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(329, 1048577, F32, 3) (dual of [1048577, 1048568, 4]-code or 1048577-cap in PG(8,32)), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(3218, 1048587, F32, 5) (dual of [1048587, 1048569, 6]-code), using
(13, 18, 1048587)-Net over F32 — Digital
Digital (13, 18, 1048587)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3218, 1048587, F32, 5) (dual of [1048587, 1048569, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(3217, 1048577, F32, 5) (dual of [1048577, 1048560, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(329, 1048577, F32, 3) (dual of [1048577, 1048568, 4]-code or 1048577-cap in PG(8,32)), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
(13, 18, large)-Net in Base 32 — Upper bound on s
There is no (13, 18, large)-net in base 32, because
- 3 times m-reduction [i] would yield (13, 15, large)-net in base 32, but