Best Known (42, 42+15, s)-Nets in Base 9
(42, 42+15, 940)-Net over F9 — Constructive and digital
Digital (42, 57, 940)-net over F9, using
- net defined by OOA [i] based on linear OOA(957, 940, F9, 15, 15) (dual of [(940, 15), 14043, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(957, 6581, F9, 15) (dual of [6581, 6524, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(953, 6561, F9, 15) (dual of [6561, 6508, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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]
- linear OA(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(957, 6581, F9, 15) (dual of [6581, 6524, 16]-code), using
(42, 42+15, 6581)-Net over F9 — Digital
Digital (42, 57, 6581)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(957, 6581, F9, 15) (dual of [6581, 6524, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(953, 6561, F9, 15) (dual of [6561, 6508, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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]
- linear OA(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
(42, 42+15, large)-Net in Base 9 — Upper bound on s
There is no (42, 57, large)-net in base 9, because
- 13 times m-reduction [i] would yield (42, 44, large)-net in base 9, but