Best Known (73−10, 73, s)-Nets in Base 3
(73−10, 73, 106288)-Net over F3 — Constructive and digital
Digital (63, 73, 106288)-net over F3, using
- net defined by OOA [i] based on linear OOA(373, 106288, F3, 10, 10) (dual of [(106288, 10), 1062807, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(373, 531440, F3, 10) (dual of [531440, 531367, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(373, 531440, F3, 10) (dual of [531440, 531367, 11]-code), using
(73−10, 73, 177147)-Net over F3 — Digital
Digital (63, 73, 177147)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(373, 177147, F3, 3, 10) (dual of [(177147, 3), 531368, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- OOA 3-folding [i] based on linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using
(73−10, 73, large)-Net in Base 3 — Upper bound on s
There is no (63, 73, large)-net in base 3, because
- 8 times m-reduction [i] would yield (63, 65, large)-net in base 3, but