Best Known (18, 18+8, s)-Nets in Base 32
(18, 18+8, 8225)-Net over F32 — Constructive and digital
Digital (18, 26, 8225)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (14, 22, 8192)-net over F32, using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- digital (0, 4, 33)-net over F32, using
(18, 18+8, 16385)-Net in Base 32 — Constructive
(18, 26, 16385)-net in base 32, using
- net defined by OOA [i] based on OOA(3226, 16385, S32, 8, 8), using
- OA 4-folding and stacking [i] based on OA(3226, 65540, S32, 8), using
- discarding factors based on OA(3226, 65541, S32, 8), using
- discarding parts of the base [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
- discarding factors based on OA(3226, 65541, S32, 8), using
- OA 4-folding and stacking [i] based on OA(3226, 65540, S32, 8), using
(18, 18+8, 42477)-Net over F32 — Digital
Digital (18, 26, 42477)-net over F32, using
(18, 18+8, large)-Net in Base 32 — Upper bound on s
There is no (18, 26, large)-net in base 32, because
- 6 times m-reduction [i] would yield (18, 20, large)-net in base 32, but