Best Known (78−5, 78, s)-Nets in Base 3
(78−5, 78, large)-Net over F3 — Constructive and digital
Digital (73, 78, large)-net over F3, using
- t-expansion [i] based on digital (72, 78, large)-net over F3, using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F27, using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F27, using
(78−5, 78, large)-Net in Base 3 — Upper bound on s
There is no (73, 78, large)-net in base 3, because
- 3 times m-reduction [i] would yield (73, 75, large)-net in base 3, but