Best Known (44−20, 44, s)-Nets in Base 128
(44−20, 44, 1640)-Net over F128 — Constructive and digital
Digital (24, 44, 1640)-net over F128, using
- net defined by OOA [i] based on linear OOA(12844, 1640, F128, 20, 20) (dual of [(1640, 20), 32756, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(12844, 16400, F128, 20) (dual of [16400, 16356, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(12844, 16400, F128, 20) (dual of [16400, 16356, 21]-code), using
(44−20, 44, 8200)-Net over F128 — Digital
Digital (24, 44, 8200)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12844, 8200, F128, 2, 20) (dual of [(8200, 2), 16356, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12844, 16400, F128, 20) (dual of [16400, 16356, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-code), using
- OOA 2-folding [i] based on linear OA(12844, 16400, F128, 20) (dual of [16400, 16356, 21]-code), using
(44−20, 44, large)-Net in Base 128 — Upper bound on s
There is no (24, 44, large)-net in base 128, because
- 18 times m-reduction [i] would yield (24, 26, large)-net in base 128, but