Best Known (74, 97, s)-Nets in Base 16
(74, 97, 11917)-Net over F16 — Constructive and digital
Digital (74, 97, 11917)-net over F16, using
- 163 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
(74, 97, 131098)-Net over F16 — Digital
Digital (74, 97, 131098)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 131098, F16, 23) (dual of [131098, 131001, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1696, 131096, F16, 23) (dual of [131096, 131000, 24]-code), using
- trace code [i] based on linear OA(25648, 65548, F256, 23) (dual of [65548, 65500, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,11]) ⊂ C([0,9]) [i] based on
- trace code [i] based on linear OA(25648, 65548, F256, 23) (dual of [65548, 65500, 24]-code), using
- linear OA(1696, 131097, F16, 22) (dual of [131097, 131001, 23]-code), using Gilbert–Varšamov bound and bm = 1696 > Vbs−1(k−1) = 28724 977570 904681 964676 160003 455160 190381 415372 822828 675817 472891 892015 834576 922403 294224 287078 770742 808619 618691 [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(1696, 131096, F16, 23) (dual of [131096, 131000, 24]-code), using
- construction X with Varšamov bound [i] based on
(74, 97, large)-Net in Base 16 — Upper bound on s
There is no (74, 97, large)-net in base 16, because
- 21 times m-reduction [i] would yield (74, 76, large)-net in base 16, but