Best Known (37, 37+6, s)-Nets in Base 9
(37, 37+6, 5592402)-Net over F9 — Constructive and digital
Digital (37, 43, 5592402)-net over F9, using
- 91 times duplication [i] based on digital (36, 42, 5592402)-net over F9, using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F81, using
- net defined by OOA [i] based on linear OOA(8121, 2796201, F81, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(8121, 2796201, F81, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- trace code for nets [i] based on digital (15, 21, 2796201)-net over F81, using
(37, 37+6, large)-Net over F9 — Digital
Digital (37, 43, large)-net over F9, using
- 94 times duplication [i] based on digital (33, 39, large)-net over F9, using
(37, 37+6, large)-Net in Base 9 — Upper bound on s
There is no (37, 43, large)-net in base 9, because
- 4 times m-reduction [i] would yield (37, 39, large)-net in base 9, but