Best Known (46, 55, s)-Nets in Base 4
(46, 55, 65536)-Net over F4 — Constructive and digital
Digital (46, 55, 65536)-net over F4, using
- net defined by OOA [i] based on linear OOA(455, 65536, F4, 9, 9) (dual of [(65536, 9), 589769, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(455, 262145, F4, 9) (dual of [262145, 262090, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(455, 262145, F4, 9) (dual of [262145, 262090, 10]-code), using
(46, 55, 131072)-Net over F4 — Digital
Digital (46, 55, 131072)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(455, 131072, F4, 2, 9) (dual of [(131072, 2), 262089, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(455, 262144, F4, 9) (dual of [262144, 262089, 10]-code), using
(46, 55, large)-Net in Base 4 — Upper bound on s
There is no (46, 55, large)-net in base 4, because
- 7 times m-reduction [i] would yield (46, 48, large)-net in base 4, but