Best Known (80, 80+17, s)-Nets in Base 16
(80, 80+17, 1048575)-Net over F16 — Constructive and digital
Digital (80, 97, 1048575)-net over F16, using
- 166 times duplication [i] based on digital (74, 91, 1048575)-net over F16, using
- net defined by OOA [i] based on linear OOA(1691, 1048575, F16, 17, 17) (dual of [(1048575, 17), 17825684, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1691, 8388601, F16, 17) (dual of [8388601, 8388510, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(1691, 8388601, F16, 17) (dual of [8388601, 8388510, 18]-code), using
- net defined by OOA [i] based on linear OOA(1691, 1048575, F16, 17, 17) (dual of [(1048575, 17), 17825684, 18]-NRT-code), using
(80, 80+17, large)-Net over F16 — Digital
Digital (80, 97, large)-net over F16, using
- 1 times m-reduction [i] based on digital (80, 98, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1698, large, F16, 18) (dual of [large, large−98, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 1 times code embedding in larger space [i] based on linear OA(1697, large, F16, 18) (dual of [large, large−97, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1698, large, F16, 18) (dual of [large, large−98, 19]-code), using
(80, 80+17, large)-Net in Base 16 — Upper bound on s
There is no (80, 97, large)-net in base 16, because
- 15 times m-reduction [i] would yield (80, 82, large)-net in base 16, but