Best Known (37, 37+24, s)-Nets in Base 128
(37, 37+24, 1515)-Net over F128 — Constructive and digital
Digital (37, 61, 1515)-net over F128, using
- 1 times m-reduction [i] based on digital (37, 62, 1515)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- 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
- digital (1, 13, 150)-net over F128, using
- (u, u+v)-construction [i] based on
(37, 37+24, 5463)-Net in Base 128 — Constructive
(37, 61, 5463)-net in base 128, using
- net defined by OOA [i] based on OOA(12861, 5463, S128, 24, 24), using
- OA 12-folding and stacking [i] based on OA(12861, 65556, S128, 24), using
- discarding parts of the base [i] based on linear OA(25653, 65556, F256, 24) (dual of [65556, 65503, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- discarding parts of the base [i] based on linear OA(25653, 65556, F256, 24) (dual of [65556, 65503, 25]-code), using
- OA 12-folding and stacking [i] based on OA(12861, 65556, S128, 24), using
(37, 37+24, 28808)-Net over F128 — Digital
Digital (37, 61, 28808)-net over F128, using
(37, 37+24, large)-Net in Base 128 — Upper bound on s
There is no (37, 61, large)-net in base 128, because
- 22 times m-reduction [i] would yield (37, 39, large)-net in base 128, but