Best Known (79, 104, s)-Nets in Base 16
(79, 104, 10924)-Net over F16 — Constructive and digital
Digital (79, 104, 10924)-net over F16, using
- 161 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
(79, 104, 131096)-Net over F16 — Digital
Digital (79, 104, 131096)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16104, 131096, F16, 25) (dual of [131096, 130992, 26]-code), using
- trace code [i] based on linear OA(25652, 65548, F256, 25) (dual of [65548, 65496, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- trace code [i] based on linear OA(25652, 65548, F256, 25) (dual of [65548, 65496, 26]-code), using
(79, 104, large)-Net in Base 16 — Upper bound on s
There is no (79, 104, large)-net in base 16, because
- 23 times m-reduction [i] would yield (79, 81, large)-net in base 16, but