Best Known (58, 74, s)-Nets in Base 32
(58, 74, 131149)-Net over F32 — Constructive and digital
Digital (58, 74, 131149)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 77)-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 (1, 9, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (45, 61, 131072)-net over F32, using
- net defined by OOA [i] based on linear OOA(3261, 131072, F32, 16, 16) (dual of [(131072, 16), 2097091, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using
- net defined by OOA [i] based on linear OOA(3261, 131072, F32, 16, 16) (dual of [(131072, 16), 2097091, 17]-NRT-code), using
- digital (5, 13, 77)-net over F32, using
(58, 74, 1048575)-Net in Base 32 — Constructive
(58, 74, 1048575)-net in base 32, using
- net defined by OOA [i] based on OOA(3274, 1048575, S32, 16, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
- discarding factors based on OA(3274, large, S32, 16), using
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding parts of the base [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- discarding factors based on OA(3274, large, S32, 16), using
- OA 8-folding and stacking [i] based on OA(3274, 8388600, S32, 16), using
(58, 74, 5518386)-Net over F32 — Digital
Digital (58, 74, 5518386)-net over F32, using
(58, 74, large)-Net in Base 32 — Upper bound on s
There is no (58, 74, large)-net in base 32, because
- 14 times m-reduction [i] would yield (58, 60, large)-net in base 32, but