Best Known (90, 90+18, s)-Nets in Base 32
(90, 90+18, 932367)-Net over F32 — Constructive and digital
Digital (90, 108, 932367)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (13, 22, 300)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 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 (8, 17, 256)-net over F32, using
- net defined by OOA [i] based on linear OOA(3217, 256, F32, 9, 9) (dual of [(256, 9), 2287, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3217, 1025, F32, 9) (dual of [1025, 1008, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(3217, 1025, F32, 9) (dual of [1025, 1008, 10]-code), using
- net defined by OOA [i] based on linear OOA(3217, 256, F32, 9, 9) (dual of [(256, 9), 2287, 10]-NRT-code), using
- digital (1, 5, 44)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (68, 86, 932067)-net over F32, using
- net defined by OOA [i] based on linear OOA(3286, 932067, F32, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3286, large, F32, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(3286, large, F32, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(3286, 932067, F32, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (13, 22, 300)-net over F32, using
(90, 90+18, 940259)-Net in Base 32 — Constructive
(90, 108, 940259)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (16, 25, 8192)-net over F32, using
- net defined by OOA [i] based on linear OOA(3225, 8192, F32, 9, 9) (dual of [(8192, 9), 73703, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3225, 32769, F32, 9) (dual of [32769, 32744, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(3225, 32769, F32, 9) (dual of [32769, 32744, 10]-code), using
- net defined by OOA [i] based on linear OOA(3225, 8192, F32, 9, 9) (dual of [(8192, 9), 73703, 10]-NRT-code), using
- (65, 83, 932067)-net in base 32, using
- net defined by OOA [i] based on OOA(3283, 932067, S32, 18, 18), using
- OA 9-folding and stacking [i] based on OA(3283, large, S32, 18), using
- discarding parts of the base [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding parts of the base [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- OA 9-folding and stacking [i] based on OA(3283, large, S32, 18), using
- net defined by OOA [i] based on OOA(3283, 932067, S32, 18, 18), using
- digital (16, 25, 8192)-net over F32, using
(90, 90+18, large)-Net over F32 — Digital
Digital (90, 108, large)-net over F32, using
- t-expansion [i] based on digital (87, 108, large)-net over F32, using
- 2 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(90, 90+18, large)-Net in Base 32 — Upper bound on s
There is no (90, 108, large)-net in base 32, because
- 16 times m-reduction [i] would yield (90, 92, large)-net in base 32, but