Best Known (250−18, 250, s)-Nets in Base 4
(250−18, 250, 3729633)-Net over F4 — Constructive and digital
Digital (232, 250, 3729633)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 42, 1365)-net over F4, using
- net defined by OOA [i] based on linear OOA(442, 1365, F4, 9, 9) (dual of [(1365, 9), 12243, 10]-NRT-code), using
- digital (190, 208, 3728268)-net over F4, using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- trace code for nets [i] based on digital (34, 52, 932067)-net over F256, using
- digital (33, 42, 1365)-net over F4, using
(250−18, 250, large)-Net over F4 — Digital
Digital (232, 250, large)-net over F4, using
- t-expansion [i] based on digital (231, 250, large)-net over F4, using
- 7 times m-reduction [i] based on digital (231, 257, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4257, large, F4, 26) (dual of [large, large−257, 27]-code), using
- 28 times code embedding in larger space [i] based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 28 times code embedding in larger space [i] based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4257, large, F4, 26) (dual of [large, large−257, 27]-code), using
- 7 times m-reduction [i] based on digital (231, 257, large)-net over F4, using
(250−18, 250, large)-Net in Base 4 — Upper bound on s
There is no (232, 250, large)-net in base 4, because
- 16 times m-reduction [i] would yield (232, 234, large)-net in base 4, but