Best Known (46, 46+12, s)-Nets in Base 16
(46, 46+12, 174765)-Net over F16 — Constructive and digital
Digital (46, 58, 174765)-net over F16, using
- net defined by OOA [i] based on linear OOA(1658, 174765, F16, 12, 12) (dual of [(174765, 12), 2097122, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(1658, 1048590, F16, 12) (dual of [1048590, 1048532, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1658, 1048593, F16, 12) (dual of [1048593, 1048535, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(1658, 1048593, F16, 12) (dual of [1048593, 1048535, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(1658, 1048590, F16, 12) (dual of [1048590, 1048532, 13]-code), using
(46, 46+12, 1048593)-Net over F16 — Digital
Digital (46, 58, 1048593)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1658, 1048593, F16, 12) (dual of [1048593, 1048535, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(11) ⊂ Ce(8) [i] based on
(46, 46+12, large)-Net in Base 16 — Upper bound on s
There is no (46, 58, large)-net in base 16, because
- 10 times m-reduction [i] would yield (46, 48, large)-net in base 16, but