Best Known (81, 81+4, s)-Nets in Base 4
(81, 81+4, large)-Net over F4 — Constructive and digital
Digital (81, 85, large)-net over F4, using
- 41 times duplication [i] based on digital (80, 84, large)-net over F4, using
- t-expansion [i] based on digital (77, 84, large)-net over F4, using
- trace code for nets [i] based on digital (21, 28, 2796265)-net over F64, using
- net defined by OOA [i] based on linear OOA(6428, 2796265, F64, 9, 7) (dual of [(2796265, 9), 25166357, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(6428, 2796266, F64, 3, 7) (dual of [(2796266, 3), 8388770, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;192,64) [i]
- linear OOA(6425, 2796201, F64, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(6428, 2796266, F64, 3, 7) (dual of [(2796266, 3), 8388770, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6428, 2796265, F64, 9, 7) (dual of [(2796265, 9), 25166357, 8]-NRT-code), using
- trace code for nets [i] based on digital (21, 28, 2796265)-net over F64, using
- t-expansion [i] based on digital (77, 84, large)-net over F4, using
(81, 81+4, large)-Net in Base 4 — Upper bound on s
There is no (81, 85, large)-net in base 4, because
- 2 times m-reduction [i] would yield (81, 83, large)-net in base 4, but