Best Known (85−23, 85, s)-Nets in Base 16
(85−23, 85, 5958)-Net over F16 — Constructive and digital
Digital (62, 85, 5958)-net over F16, using
- net defined by OOA [i] based on linear OOA(1685, 5958, F16, 23, 23) (dual of [(5958, 23), 136949, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1685, 65539, F16, 23) (dual of [65539, 65454, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1685, 65540, F16, 23) (dual of [65540, 65455, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(1685, 65540, F16, 23) (dual of [65540, 65455, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1685, 65539, F16, 23) (dual of [65539, 65454, 24]-code), using
(85−23, 85, 37910)-Net over F16 — Digital
Digital (62, 85, 37910)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1685, 37910, F16, 23) (dual of [37910, 37825, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using
(85−23, 85, large)-Net in Base 16 — Upper bound on s
There is no (62, 85, large)-net in base 16, because
- 21 times m-reduction [i] would yield (62, 64, large)-net in base 16, but