Best Known (69, 69+25, s)-Nets in Base 16
(69, 69+25, 5462)-Net over F16 — Constructive and digital
Digital (69, 94, 5462)-net over F16, using
- net defined by OOA [i] based on linear OOA(1694, 5462, F16, 25, 25) (dual of [(5462, 25), 136456, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
(69, 69+25, 46461)-Net over F16 — Digital
Digital (69, 94, 46461)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1694, 46461, F16, 25) (dual of [46461, 46367, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
(69, 69+25, large)-Net in Base 16 — Upper bound on s
There is no (69, 94, large)-net in base 16, because
- 23 times m-reduction [i] would yield (69, 71, large)-net in base 16, but