Best Known (34, 50, s)-Nets in Base 256
(34, 50, 1048575)-Net over F256 — Constructive and digital
Digital (34, 50, 1048575)-net over F256, using
- 2561 times duplication [i] based on digital (33, 49, 1048575)-net over F256, using
- t-expansion [i] based on digital (32, 49, 1048575)-net over F256, using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25649, 8388601, F256, 17) (dual of [8388601, 8388552, 18]-code), using
- net defined by OOA [i] based on linear OOA(25649, 1048575, F256, 17, 17) (dual of [(1048575, 17), 17825726, 18]-NRT-code), using
- t-expansion [i] based on digital (32, 49, 1048575)-net over F256, using
(34, 50, 6364394)-Net over F256 — Digital
Digital (34, 50, 6364394)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25650, 6364394, F256, 16) (dual of [6364394, 6364344, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25650, large, F256, 16) (dual of [large, large−50, 17]-code), using
- 4 times code embedding in larger space [i] 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]
- 4 times code embedding in larger space [i] based on linear OA(25646, large, F256, 16) (dual of [large, large−46, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(25650, large, F256, 16) (dual of [large, large−50, 17]-code), using
(34, 50, large)-Net in Base 256 — Upper bound on s
There is no (34, 50, large)-net in base 256, because
- 14 times m-reduction [i] would yield (34, 36, large)-net in base 256, but