Best Known (38, 48, s)-Nets in Base 16
(38, 48, 209718)-Net over F16 — Constructive and digital
Digital (38, 48, 209718)-net over F16, using
- net defined by OOA [i] based on linear OOA(1648, 209718, F16, 10, 10) (dual of [(209718, 10), 2097132, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1648, 1048590, F16, 10) (dual of [1048590, 1048542, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1648, 1048593, F16, 10) (dual of [1048593, 1048545, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(1648, 1048593, F16, 10) (dual of [1048593, 1048545, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(1648, 1048590, F16, 10) (dual of [1048590, 1048542, 11]-code), using
(38, 48, 1048593)-Net over F16 — Digital
Digital (38, 48, 1048593)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1648, 1048593, F16, 10) (dual of [1048593, 1048545, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
(38, 48, large)-Net in Base 16 — Upper bound on s
There is no (38, 48, large)-net in base 16, because
- 8 times m-reduction [i] would yield (38, 40, large)-net in base 16, but