Best Known (110−26, 110, s)-Nets in Base 16
(110−26, 110, 10084)-Net over F16 — Constructive and digital
Digital (84, 110, 10084)-net over F16, using
- 162 times duplication [i] based on digital (82, 108, 10084)-net over F16, using
- net defined by OOA [i] based on linear OOA(16108, 10084, F16, 26, 26) (dual of [(10084, 26), 262076, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16108, 131092, F16, 26) (dual of [131092, 130984, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16108, 131094, F16, 26) (dual of [131094, 130986, 27]-code), using
- trace code [i] based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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 Ce(25) ⊂ Ce(21) [i] based on
- trace code [i] based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16108, 131094, F16, 26) (dual of [131094, 130986, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(16108, 131092, F16, 26) (dual of [131092, 130984, 27]-code), using
- net defined by OOA [i] based on linear OOA(16108, 10084, F16, 26, 26) (dual of [(10084, 26), 262076, 27]-NRT-code), using
(110−26, 110, 134804)-Net over F16 — Digital
Digital (84, 110, 134804)-net over F16, using
(110−26, 110, large)-Net in Base 16 — Upper bound on s
There is no (84, 110, large)-net in base 16, because
- 24 times m-reduction [i] would yield (84, 86, large)-net in base 16, but