Best Known (34, 34+20, s)-Nets in Base 128
(34, 34+20, 1896)-Net over F128 — Constructive and digital
Digital (34, 54, 1896)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 258)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (0, 10, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 5, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (19, 39, 1638)-net over F128, using
- net defined by OOA [i] based on linear OOA(12839, 1638, F128, 20, 20) (dual of [(1638, 20), 32721, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(12839, 16380, F128, 20) (dual of [16380, 16341, 21]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(12839, 16380, F128, 20) (dual of [16380, 16341, 21]-code), using
- net defined by OOA [i] based on linear OOA(12839, 1638, F128, 20, 20) (dual of [(1638, 20), 32721, 21]-NRT-code), using
- digital (5, 15, 258)-net over F128, using
(34, 34+20, 6556)-Net in Base 128 — Constructive
(34, 54, 6556)-net in base 128, using
- net defined by OOA [i] based on OOA(12854, 6556, S128, 20, 20), using
- OA 10-folding and stacking [i] based on OA(12854, 65560, S128, 20), using
- discarding factors based on OA(12854, 65562, S128, 20), using
- discarding parts of the base [i] based on linear OA(25647, 65562, F256, 20) (dual of [65562, 65515, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(25647, 65562, F256, 20) (dual of [65562, 65515, 21]-code), using
- discarding factors based on OA(12854, 65562, S128, 20), using
- OA 10-folding and stacking [i] based on OA(12854, 65560, S128, 20), using
(34, 34+20, 60868)-Net over F128 — Digital
Digital (34, 54, 60868)-net over F128, using
(34, 34+20, large)-Net in Base 128 — Upper bound on s
There is no (34, 54, large)-net in base 128, because
- 18 times m-reduction [i] would yield (34, 36, large)-net in base 128, but