Best Known (72−5, 72, s)-Nets in Base 4
(72−5, 72, large)-Net over F4 — Constructive and digital
Digital (67, 72, large)-net over F4, using
- 49 times duplication [i] based on digital (58, 63, large)-net over F4, using
- t-expansion [i] based on digital (57, 63, large)-net over F4, using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F64, using
- t-expansion [i] based on digital (57, 63, large)-net over F4, using
(72−5, 72, large)-Net in Base 4 — Upper bound on s
There is no (67, 72, large)-net in base 4, because
- 3 times m-reduction [i] would yield (67, 69, large)-net in base 4, but