Best Known (37, 57, s)-Nets in Base 32
(37, 57, 363)-Net over F32 — Constructive and digital
Digital (37, 57, 363)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 10, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 20, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(37, 57, 1639)-Net in Base 32 — Constructive
(37, 57, 1639)-net in base 32, using
- net defined by OOA [i] based on OOA(3257, 1639, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3257, 16390, S32, 20), using
- 1 times code embedding in larger space [i] based on OA(3256, 16389, S32, 20), using
- discarding parts of the base [i] based on linear OA(12840, 16389, F128, 20) (dual of [16389, 16349, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] 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]
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(12840, 16389, F128, 20) (dual of [16389, 16349, 21]-code), using
- 1 times code embedding in larger space [i] based on OA(3256, 16389, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3257, 16390, S32, 20), using
(37, 57, 8391)-Net over F32 — Digital
Digital (37, 57, 8391)-net over F32, using
(37, 57, large)-Net in Base 32 — Upper bound on s
There is no (37, 57, large)-net in base 32, because
- 18 times m-reduction [i] would yield (37, 39, large)-net in base 32, but