Best Known (126−35, 126, s)-Nets in Base 16
(126−35, 126, 1542)-Net over F16 — Constructive and digital
Digital (91, 126, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (11, 22, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 11, 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, 11, 257)-net over F256, using
- digital (17, 34, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 17, 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, 17, 257)-net over F256, using
- digital (35, 70, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 35, 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, 35, 257)-net over F256, using
- digital (11, 22, 514)-net over F16, using
(126−35, 126, 1927)-Net in Base 16 — Constructive
(91, 126, 1927)-net in base 16, using
- 161 times duplication [i] based on (90, 125, 1927)-net in base 16, using
- base change [i] based on digital (65, 100, 1927)-net over F32, using
- net defined by OOA [i] based on linear OOA(32100, 1927, F32, 35, 35) (dual of [(1927, 35), 67345, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
- net defined by OOA [i] based on linear OOA(32100, 1927, F32, 35, 35) (dual of [(1927, 35), 67345, 36]-NRT-code), using
- base change [i] based on digital (65, 100, 1927)-net over F32, using
(126−35, 126, 26181)-Net over F16 — Digital
Digital (91, 126, 26181)-net over F16, using
(126−35, 126, large)-Net in Base 16 — Upper bound on s
There is no (91, 126, large)-net in base 16, because
- 33 times m-reduction [i] would yield (91, 93, large)-net in base 16, but