Best Known (38−11, 38, s)-Nets in Base 16
(38−11, 38, 1542)-Net over F16 — Constructive and digital
Digital (27, 38, 1542)-net over F16, using
- 161 times duplication [i] based on digital (26, 37, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 5, 514)-net over F16, using
- s-reduction based on digital (2, 5, 629)-net over F16, using
- net defined by OOA [i] based on linear OOA(165, 629, F16, 3, 3) (dual of [(629, 3), 1882, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(165, 629, F16, 2, 3) (dual of [(629, 2), 1253, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(165, 629, F16, 3, 3) (dual of [(629, 3), 1882, 4]-NRT-code), using
- s-reduction based on digital (2, 5, 629)-net over F16, using
- digital (5, 10, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 5, 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, 5, 257)-net over F256, using
- 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 (see above)
- trace code for nets [i] based on digital (0, 11, 257)-net over F256, using
- digital (2, 5, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(38−11, 38, 3277)-Net in Base 16 — Constructive
(27, 38, 3277)-net in base 16, using
- 161 times duplication [i] based on (26, 37, 3277)-net in base 16, using
- net defined by OOA [i] based on OOA(1637, 3277, S16, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(1637, 16386, S16, 11), using
- discarding parts of the base [i] based on linear OA(12821, 16386, F128, 11) (dual of [16386, 16365, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(12821, 16386, F128, 11) (dual of [16386, 16365, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on OA(1637, 16386, S16, 11), using
- net defined by OOA [i] based on OOA(1637, 3277, S16, 11, 11), using
(38−11, 38, 11369)-Net over F16 — Digital
Digital (27, 38, 11369)-net over F16, using
(38−11, 38, large)-Net in Base 16 — Upper bound on s
There is no (27, 38, large)-net in base 16, because
- 9 times m-reduction [i] would yield (27, 29, large)-net in base 16, but