Best Known (148−25, 148, s)-Nets in Base 8
(148−25, 148, 174762)-Net over F8 — Constructive and digital
Digital (123, 148, 174762)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 174762, F8, 25, 25) (dual of [(174762, 25), 4368902, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
(148−25, 148, 1048576)-Net over F8 — Digital
Digital (123, 148, 1048576)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8148, 1048576, F8, 2, 25) (dual of [(1048576, 2), 2097004, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 2-folding [i] based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
(148−25, 148, large)-Net in Base 8 — Upper bound on s
There is no (123, 148, large)-net in base 8, because
- 23 times m-reduction [i] would yield (123, 125, large)-net in base 8, but