Best Known (36, 36+20, s)-Nets in Base 32
(36, 36+20, 330)-Net over F32 — Constructive and digital
Digital (36, 56, 330)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- 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)
(36, 36+20, 1638)-Net in Base 32 — Constructive
(36, 56, 1638)-net in base 32, using
- base change [i] based on digital (20, 40, 1638)-net over F128, using
- 1 times m-reduction [i] based on digital (20, 41, 1638)-net over F128, using
- net defined by OOA [i] based on linear OOA(12841, 1638, F128, 21, 21) (dual of [(1638, 21), 34357, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12841, 16381, F128, 21) (dual of [16381, 16340, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12841, 16381, F128, 21) (dual of [16381, 16340, 22]-code), using
- net defined by OOA [i] based on linear OOA(12841, 1638, F128, 21, 21) (dual of [(1638, 21), 34357, 22]-NRT-code), using
- 1 times m-reduction [i] based on digital (20, 41, 1638)-net over F128, using
(36, 36+20, 6993)-Net over F32 — Digital
Digital (36, 56, 6993)-net over F32, using
(36, 36+20, large)-Net in Base 32 — Upper bound on s
There is no (36, 56, large)-net in base 32, because
- 18 times m-reduction [i] would yield (36, 38, large)-net in base 32, but