Best Known (105−28, 105, s)-Nets in Base 16
(105−28, 105, 4681)-Net over F16 — Constructive and digital
Digital (77, 105, 4681)-net over F16, using
- net defined by OOA [i] based on linear OOA(16105, 4681, F16, 28, 28) (dual of [(4681, 28), 130963, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16105, 65534, F16, 28) (dual of [65534, 65429, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16105, 65534, F16, 28) (dual of [65534, 65429, 29]-code), using
(105−28, 105, 46084)-Net over F16 — Digital
Digital (77, 105, 46084)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16105, 46084, F16, 28) (dual of [46084, 45979, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using
(105−28, 105, large)-Net in Base 16 — Upper bound on s
There is no (77, 105, large)-net in base 16, because
- 26 times m-reduction [i] would yield (77, 79, large)-net in base 16, but