Best Known (78, 78+16, s)-Nets in Base 16
(78, 78+16, 2097150)-Net over F16 — Constructive and digital
Digital (78, 94, 2097150)-net over F16, using
- 162 times duplication [i] based on digital (76, 92, 2097150)-net over F16, using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- OOA 2-folding [i] based on linear OA(25646, 8388602, F256, 16) (dual of [8388602, 8388556, 17]-code), using
- trace code [i] based on linear OOA(25646, 4194301, F256, 2, 16) (dual of [(4194301, 2), 8388556, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1692, 8388602, F16, 2, 16) (dual of [(8388602, 2), 16777112, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(1692, 8388601, F16, 2, 16) (dual of [(8388601, 2), 16777110, 17]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1692, 2097150, F16, 18, 16) (dual of [(2097150, 18), 37748608, 17]-NRT-code), using
(78, 78+16, large)-Net over F16 — Digital
Digital (78, 94, large)-net over F16, using
- 162 times duplication [i] based on digital (76, 92, large)-net over F16, using
- t-expansion [i] based on digital (75, 92, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1692, large, F16, 17) (dual of [large, large−92, 18]-code), using
- 1 times code embedding in larger space [i] 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]
- 1 times code embedding in larger space [i] based on linear OA(1691, large, F16, 17) (dual of [large, large−91, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1692, large, F16, 17) (dual of [large, large−92, 18]-code), using
- t-expansion [i] based on digital (75, 92, large)-net over F16, using
(78, 78+16, large)-Net in Base 16 — Upper bound on s
There is no (78, 94, large)-net in base 16, because
- 14 times m-reduction [i] would yield (78, 80, large)-net in base 16, but