Best Known (47, 65, s)-Nets in Base 16
(47, 65, 7282)-Net over F16 — Constructive and digital
Digital (47, 65, 7282)-net over F16, using
- net defined by OOA [i] based on linear OOA(1665, 7282, F16, 18, 18) (dual of [(7282, 18), 131011, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(1665, 65538, F16, 18) (dual of [65538, 65473, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(1665, 65536, F16, 18) (dual of [65536, 65471, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(1665, 65538, F16, 18) (dual of [65538, 65473, 19]-code), using
(47, 65, 32770)-Net over F16 — Digital
Digital (47, 65, 32770)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1665, 32770, F16, 2, 18) (dual of [(32770, 2), 65475, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(1665, 65536, F16, 18) (dual of [65536, 65471, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(17) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(1665, 65540, F16, 18) (dual of [65540, 65475, 19]-code), using
(47, 65, large)-Net in Base 16 — Upper bound on s
There is no (47, 65, large)-net in base 16, because
- 16 times m-reduction [i] would yield (47, 49, large)-net in base 16, but