Best Known (74, 74+24, s)-Nets in Base 16
(74, 74+24, 10924)-Net over F16 — Constructive and digital
Digital (74, 98, 10924)-net over F16, using
- net defined by OOA [i] based on linear OOA(1698, 10924, F16, 24, 24) (dual of [(10924, 24), 262078, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(1698, 131088, F16, 24) (dual of [131088, 130990, 25]-code), using
- trace code [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(1698, 131088, F16, 24) (dual of [131088, 130990, 25]-code), using
(74, 74+24, 122969)-Net over F16 — Digital
Digital (74, 98, 122969)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1698, 122969, F16, 24) (dual of [122969, 122871, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131088, F16, 24) (dual of [131088, 130990, 25]-code), using
- trace code [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(23) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(25649, 65544, F256, 24) (dual of [65544, 65495, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131088, F16, 24) (dual of [131088, 130990, 25]-code), using
(74, 74+24, large)-Net in Base 16 — Upper bound on s
There is no (74, 98, large)-net in base 16, because
- 22 times m-reduction [i] would yield (74, 76, large)-net in base 16, but