Best Known (60, 60+15, s)-Nets in Base 16
(60, 60+15, 149800)-Net over F16 — Constructive and digital
Digital (60, 75, 149800)-net over F16, using
- net defined by OOA [i] based on linear OOA(1675, 149800, F16, 15, 15) (dual of [(149800, 15), 2246925, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(1675, 1048601, F16, 15) (dual of [1048601, 1048526, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(1671, 1048577, F16, 15) (dual of [1048577, 1048506, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(1651, 1048577, F16, 11) (dual of [1048577, 1048526, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(1675, 1048601, F16, 15) (dual of [1048601, 1048526, 16]-code), using
(60, 60+15, 1137658)-Net over F16 — Digital
Digital (60, 75, 1137658)-net over F16, using
(60, 60+15, large)-Net in Base 16 — Upper bound on s
There is no (60, 75, large)-net in base 16, because
- 13 times m-reduction [i] would yield (60, 62, large)-net in base 16, but