Best Known (48, 60, s)-Nets in Base 16
(48, 60, 174766)-Net over F16 — Constructive and digital
Digital (48, 60, 174766)-net over F16, using
- net defined by OOA [i] based on linear OOA(1660, 174766, F16, 12, 12) (dual of [(174766, 12), 2097132, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(1660, 1048596, F16, 12) (dual of [1048596, 1048536, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1660, 1048600, F16, 12) (dual of [1048600, 1048540, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(1660, 1048600, F16, 12) (dual of [1048600, 1048540, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(1660, 1048596, F16, 12) (dual of [1048596, 1048536, 13]-code), using
(48, 60, 349525)-Net in Base 16 — Constructive
(48, 60, 349525)-net in base 16, using
- net defined by OOA [i] based on OOA(1660, 349525, S16, 12, 12), using
- OA 6-folding and stacking [i] based on OA(1660, 2097150, S16, 12), using
- discarding factors based on OA(1660, 2097155, S16, 12), using
- discarding parts of the base [i] based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- discarding factors based on OA(1660, 2097155, S16, 12), using
- OA 6-folding and stacking [i] based on OA(1660, 2097150, S16, 12), using
(48, 60, 1210186)-Net over F16 — Digital
Digital (48, 60, 1210186)-net over F16, using
(48, 60, large)-Net in Base 16 — Upper bound on s
There is no (48, 60, large)-net in base 16, because
- 10 times m-reduction [i] would yield (48, 50, large)-net in base 16, but