Best Known (191−15, 191, s)-Nets in Base 4
(191−15, 191, 4793555)-Net over F4 — Constructive and digital
Digital (176, 191, 4793555)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (12, 19, 71)-net over F4, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 17)-net over F4, using
- s-reduction based on digital (0, 1, s)-net over F4 with arbitrarily large s, using
- digital (1, 3, 17)-net over F4, using
- s-reduction based on digital (1, 3, 21)-net over F4, using
- digital (1, 4, 17)-net over F4, using
- net defined by OOA [i] based on linear OOA(44, 17, F4, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
- digital (4, 11, 20)-net over F4, using
- digital (0, 1, 17)-net over F4, using
- generalized (u, u+v)-construction [i] based on
- digital (157, 172, 4793484)-net over F4, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- digital (12, 19, 71)-net over F4, using
(191−15, 191, large)-Net over F4 — Digital
Digital (176, 191, large)-net over F4, using
- 45 times duplication [i] based on digital (171, 186, large)-net over F4, using
- t-expansion [i] based on digital (167, 186, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- t-expansion [i] based on digital (167, 186, large)-net over F4, using
(191−15, 191, large)-Net in Base 4 — Upper bound on s
There is no (176, 191, large)-net in base 4, because
- 13 times m-reduction [i] would yield (176, 178, large)-net in base 4, but