Best Known (39, 53, s)-Nets in Base 16
(39, 53, 9362)-Net over F16 — Constructive and digital
Digital (39, 53, 9362)-net over F16, using
- net defined by OOA [i] based on linear OOA(1653, 9362, F16, 14, 14) (dual of [(9362, 14), 131015, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(1653, 65534, F16, 14) (dual of [65534, 65481, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(1653, 65534, F16, 14) (dual of [65534, 65481, 15]-code), using
(39, 53, 58221)-Net over F16 — Digital
Digital (39, 53, 58221)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1653, 58221, F16, 14) (dual of [58221, 58168, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(1653, 65536, F16, 14) (dual of [65536, 65483, 15]-code), using
(39, 53, large)-Net in Base 16 — Upper bound on s
There is no (39, 53, large)-net in base 16, because
- 12 times m-reduction [i] would yield (39, 41, large)-net in base 16, but