Best Known (24, 24+24, s)-Nets in Base 128
(24, 24+24, 1365)-Net over F128 — Constructive and digital
Digital (24, 48, 1365)-net over F128, using
- 1 times m-reduction [i] based on digital (24, 49, 1365)-net over F128, using
- net defined by OOA [i] based on linear OOA(12849, 1365, F128, 25, 25) (dual of [(1365, 25), 34076, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12849, 16381, F128, 25) (dual of [16381, 16332, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(12849, 16384, F128, 25) (dual of [16384, 16335, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(12849, 16384, F128, 25) (dual of [16384, 16335, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(12849, 16381, F128, 25) (dual of [16381, 16332, 26]-code), using
- net defined by OOA [i] based on linear OOA(12849, 1365, F128, 25, 25) (dual of [(1365, 25), 34076, 26]-NRT-code), using
(24, 24+24, 4097)-Net over F128 — Digital
Digital (24, 48, 4097)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12848, 4097, F128, 4, 24) (dual of [(4097, 4), 16340, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12848, 16388, F128, 24) (dual of [16388, 16340, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12848, 16389, F128, 24) (dual of [16389, 16341, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(12848, 16389, F128, 24) (dual of [16389, 16341, 25]-code), using
- OOA 4-folding [i] based on linear OA(12848, 16388, F128, 24) (dual of [16388, 16340, 25]-code), using
(24, 24+24, large)-Net in Base 128 — Upper bound on s
There is no (24, 48, large)-net in base 128, because
- 22 times m-reduction [i] would yield (24, 26, large)-net in base 128, but