Best Known (81, 81+25, s)-Nets in Base 16
(81, 81+25, 10924)-Net over F16 — Constructive and digital
Digital (81, 106, 10924)-net over F16, using
- 163 times duplication [i] based on digital (78, 103, 10924)-net over F16, using
- net defined by OOA [i] based on linear OOA(16103, 10924, F16, 25, 25) (dual of [(10924, 25), 272997, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16103, 131089, F16, 25) (dual of [131089, 130986, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16102, 131088, F16, 25) (dual of [131088, 130986, 26]-code), using
- trace code [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- trace code [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16102, 131088, F16, 25) (dual of [131088, 130986, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16103, 131089, F16, 25) (dual of [131089, 130986, 26]-code), using
- net defined by OOA [i] based on linear OOA(16103, 10924, F16, 25, 25) (dual of [(10924, 25), 272997, 26]-NRT-code), using
(81, 81+25, 135990)-Net over F16 — Digital
Digital (81, 106, 135990)-net over F16, using
(81, 81+25, large)-Net in Base 16 — Upper bound on s
There is no (81, 106, large)-net in base 16, because
- 23 times m-reduction [i] would yield (81, 83, large)-net in base 16, but