Best Known (82, 82+25, s)-Nets in Base 16
(82, 82+25, 10925)-Net over F16 — Constructive and digital
Digital (82, 107, 10925)-net over F16, using
- net defined by OOA [i] based on linear OOA(16107, 10925, F16, 25, 25) (dual of [(10925, 25), 273018, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16107, 131101, F16, 25) (dual of [131101, 130994, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16106, 131100, F16, 25) (dual of [131100, 130994, 26]-code), using
- trace code [i] based on linear OA(25653, 65550, F256, 25) (dual of [65550, 65497, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [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(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(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(25653, 65550, F256, 25) (dual of [65550, 65497, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(16106, 131100, F16, 25) (dual of [131100, 130994, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16107, 131101, F16, 25) (dual of [131101, 130994, 26]-code), using
(82, 82+25, 152642)-Net over F16 — Digital
Digital (82, 107, 152642)-net over F16, using
(82, 82+25, large)-Net in Base 16 — Upper bound on s
There is no (82, 107, large)-net in base 16, because
- 23 times m-reduction [i] would yield (82, 84, large)-net in base 16, but