Best Known (124, 124+24, s)-Nets in Base 9
(124, 124+24, 398581)-Net over F9 — Constructive and digital
Digital (124, 148, 398581)-net over F9, using
- net defined by OOA [i] based on linear OOA(9148, 398581, F9, 24, 24) (dual of [(398581, 24), 9565796, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9148, 4782972, F9, 24) (dual of [4782972, 4782824, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9148, 4782976, F9, 24) (dual of [4782976, 4782828, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(9148, 4782969, F9, 24) (dual of [4782969, 4782821, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9148, 4782976, F9, 24) (dual of [4782976, 4782828, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9148, 4782972, F9, 24) (dual of [4782972, 4782824, 25]-code), using
(124, 124+24, 2690518)-Net over F9 — Digital
Digital (124, 148, 2690518)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9148, 2690518, F9, 24) (dual of [2690518, 2690370, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9148, 4782969, F9, 24) (dual of [4782969, 4782821, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(9148, 4782969, F9, 24) (dual of [4782969, 4782821, 25]-code), using
(124, 124+24, large)-Net in Base 9 — Upper bound on s
There is no (124, 148, large)-net in base 9, because
- 22 times m-reduction [i] would yield (124, 126, large)-net in base 9, but