Best Known (44−6, 44, s)-Nets in Base 8
(44−6, 44, 5592402)-Net over F8 — Constructive and digital
Digital (38, 44, 5592402)-net over F8, using
- 82 times duplication [i] based on digital (36, 42, 5592402)-net over F8, 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
(44−6, 44, large)-Net over F8 — Digital
Digital (38, 44, large)-net over F8, using
- 83 times duplication [i] based on digital (35, 41, large)-net over F8, using
(44−6, 44, large)-Net in Base 8 — Upper bound on s
There is no (38, 44, large)-net in base 8, because
- 4 times m-reduction [i] would yield (38, 40, large)-net in base 8, but