Best Known (29, 45, s)-Nets in Base 32
(29, 45, 363)-Net over F32 — Constructive and digital
Digital (29, 45, 363)-net over F32, using
- 1 times m-reduction [i] based on digital (29, 46, 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, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- 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, 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, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 17, 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
- generalized (u, u+v)-construction [i] based on
(29, 45, 2048)-Net in Base 32 — Constructive
(29, 45, 2048)-net in base 32, using
- 321 times duplication [i] based on (28, 44, 2048)-net in base 32, using
- net defined by OOA [i] based on OOA(3244, 2048, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3244, 16384, S32, 16), using
- discarding factors based on OA(3244, 16386, S32, 16), using
- discarding parts of the base [i] based on linear OA(12831, 16386, F128, 16) (dual of [16386, 16355, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(15) ⊂ Ce(14) [i] based on
- discarding parts of the base [i] based on linear OA(12831, 16386, F128, 16) (dual of [16386, 16355, 17]-code), using
- discarding factors based on OA(3244, 16386, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3244, 16384, S32, 16), using
- net defined by OOA [i] based on OOA(3244, 2048, S32, 16, 16), using
(29, 45, 6797)-Net over F32 — Digital
Digital (29, 45, 6797)-net over F32, using
(29, 45, large)-Net in Base 32 — Upper bound on s
There is no (29, 45, large)-net in base 32, because
- 14 times m-reduction [i] would yield (29, 31, large)-net in base 32, but