Best Known (16, 20, s)-Nets in Base 16
(16, 20, 8388602)-Net over F16 — Constructive and digital
Digital (16, 20, 8388602)-net over F16, using
- trace code for nets [i] based on digital (6, 10, 4194301)-net over F256, using
- net defined by OOA [i] based on linear OOA(25610, 4194301, F256, 4, 4) (dual of [(4194301, 4), 16777194, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(25610, large, F256, 4) (dual of [large, large−10, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(25610, 8388602, F256, 4) (dual of [8388602, 8388592, 5]-code), using
- net defined by OOA [i] based on linear OOA(25610, 4194301, F256, 4, 4) (dual of [(4194301, 4), 16777194, 5]-NRT-code), using
(16, 20, large)-Net over F16 — Digital
Digital (16, 20, large)-net over F16, using
- 161 times duplication [i] based on digital (15, 19, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1619, large, F16, 4) (dual of [large, large−19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1619, large, F16, 4) (dual of [large, large−19, 5]-code), using
(16, 20, large)-Net in Base 16 — Upper bound on s
There is no (16, 20, large)-net in base 16, because
- 2 times m-reduction [i] would yield (16, 18, large)-net in base 16, but