Best Known (80, 109, s)-Nets in Base 16
(80, 109, 4681)-Net over F16 — Constructive and digital
Digital (80, 109, 4681)-net over F16, using
- net defined by OOA [i] based on linear OOA(16109, 4681, F16, 29, 29) (dual of [(4681, 29), 135640, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16109, 65535, F16, 29) (dual of [65535, 65426, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16109, 65535, F16, 29) (dual of [65535, 65426, 30]-code), using
(80, 109, 47716)-Net over F16 — Digital
Digital (80, 109, 47716)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16109, 47716, F16, 29) (dual of [47716, 47607, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using
(80, 109, large)-Net in Base 16 — Upper bound on s
There is no (80, 109, large)-net in base 16, because
- 27 times m-reduction [i] would yield (80, 82, large)-net in base 16, but