Best Known (72, 95, s)-Nets in Base 16
(72, 95, 11917)-Net over F16 — Constructive and digital
Digital (72, 95, 11917)-net over F16, using
- 161 times duplication [i] based on digital (71, 94, 11917)-net over F16, using
- net defined by OOA [i] based on linear OOA(1694, 11917, F16, 23, 23) (dual of [(11917, 23), 273997, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1694, 131088, F16, 23) (dual of [131088, 130994, 24]-code), using
- trace code [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1694, 131088, F16, 23) (dual of [131088, 130994, 24]-code), using
- net defined by OOA [i] based on linear OOA(1694, 11917, F16, 23, 23) (dual of [(11917, 23), 273997, 24]-NRT-code), using
(72, 95, 131090)-Net over F16 — Digital
Digital (72, 95, 131090)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1695, 131090, F16, 23) (dual of [131090, 130995, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1694, 131088, F16, 23) (dual of [131088, 130994, 24]-code), using
- trace code [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(25647, 65544, F256, 23) (dual of [65544, 65497, 24]-code), using
- linear OA(1694, 131089, F16, 22) (dual of [131089, 130995, 23]-code), using Gilbert–Varšamov bound and bm = 1694 > Vbs−1(k−1) = 28688 186076 688294 813197 073108 776970 309583 214521 170540 613151 607915 209304 261779 044414 189018 271912 565075 876094 058496 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 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
- linear OA(1694, 131088, F16, 23) (dual of [131088, 130994, 24]-code), using
- construction X with Varšamov bound [i] based on
(72, 95, large)-Net in Base 16 — Upper bound on s
There is no (72, 95, large)-net in base 16, because
- 21 times m-reduction [i] would yield (72, 74, large)-net in base 16, but