Best Known (87, 87+32, s)-Nets in Base 16
(87, 87+32, 1544)-Net over F16 — Constructive and digital
Digital (87, 119, 1544)-net over F16, using
- 161 times duplication [i] based on digital (86, 118, 1544)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (10, 20, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 10, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 10, 257)-net over F256, using
- digital (16, 32, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- digital (34, 66, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 33, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 33, 258)-net over F256, using
- digital (10, 20, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(87, 87+32, 2048)-Net in Base 16 — Constructive
(87, 119, 2048)-net in base 16, using
- 1 times m-reduction [i] based on (87, 120, 2048)-net in base 16, using
- base change [i] based on digital (63, 96, 2048)-net over F32, using
- 321 times duplication [i] based on digital (62, 95, 2048)-net over F32, using
- net defined by OOA [i] based on linear OOA(3295, 2048, F32, 33, 33) (dual of [(2048, 33), 67489, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3295, 32769, F32, 33) (dual of [32769, 32674, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(321, 4, F32, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3295, 32769, F32, 33) (dual of [32769, 32674, 34]-code), using
- net defined by OOA [i] based on linear OOA(3295, 2048, F32, 33, 33) (dual of [(2048, 33), 67489, 34]-NRT-code), using
- 321 times duplication [i] based on digital (62, 95, 2048)-net over F32, using
- base change [i] based on digital (63, 96, 2048)-net over F32, using
(87, 87+32, 34706)-Net over F16 — Digital
Digital (87, 119, 34706)-net over F16, using
(87, 87+32, large)-Net in Base 16 — Upper bound on s
There is no (87, 119, large)-net in base 16, because
- 30 times m-reduction [i] would yield (87, 89, large)-net in base 16, but