Best Known (118, 141, s)-Nets in Base 9
(118, 141, 434815)-Net over F9 — Constructive and digital
Digital (118, 141, 434815)-net over F9, using
- net defined by OOA [i] based on linear OOA(9141, 434815, F9, 23, 23) (dual of [(434815, 23), 10000604, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9141, 4782966, F9, 23) (dual of [4782966, 4782825, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9141, 4782969, F9, 23) (dual of [4782969, 4782828, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(9141, 4782969, F9, 23) (dual of [4782969, 4782828, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9141, 4782966, F9, 23) (dual of [4782966, 4782825, 24]-code), using
(118, 141, 2494694)-Net over F9 — Digital
Digital (118, 141, 2494694)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9141, 2494694, F9, 23) (dual of [2494694, 2494553, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9141, 4782969, F9, 23) (dual of [4782969, 4782828, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(9141, 4782969, F9, 23) (dual of [4782969, 4782828, 24]-code), using
(118, 141, large)-Net in Base 9 — Upper bound on s
There is no (118, 141, large)-net in base 9, because
- 21 times m-reduction [i] would yield (118, 120, large)-net in base 9, but