Best Known (26, 37, s)-Nets in Base 9
(26, 37, 1312)-Net over F9 — Constructive and digital
Digital (26, 37, 1312)-net over F9, using
- net defined by OOA [i] based on linear OOA(937, 1312, F9, 11, 11) (dual of [(1312, 11), 14395, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using
(26, 37, 3397)-Net over F9 — Digital
Digital (26, 37, 3397)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(937, 3397, F9, 11) (dual of [3397, 3360, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(937, 6561, F9, 11) (dual of [6561, 6524, 12]-code), using
(26, 37, 2417084)-Net in Base 9 — Upper bound on s
There is no (26, 37, 2417085)-net in base 9, because
- 1 times m-reduction [i] would yield (26, 36, 2417085)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 22528 416323 072257 902355 344144 648457 > 936 [i]