Best Known (25, 31, s)-Nets in Base 32
(25, 31, 2799337)-Net over F32 — Constructive and digital
Digital (25, 31, 2799337)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 3136)-net over F32, using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(325, 3136, F32, 2, 3) (dual of [(3136, 2), 6267, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- digital (20, 26, 2796201)-net over F32, using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(3226, large, F32, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(3226, 2796201, F32, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- digital (2, 5, 3136)-net over F32, using
(25, 31, 2800298)-Net in Base 32 — Constructive
(25, 31, 2800298)-net in base 32, using
- 321 times duplication [i] based on (24, 30, 2800298)-net in base 32, using
- base change [i] based on digital (19, 25, 2800298)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 4097)-net over F64, using
- net defined by OOA [i] based on linear OOA(644, 4097, F64, 3, 3) (dual of [(4097, 3), 12287, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(644, 4097, F64, 2, 3) (dual of [(4097, 2), 8190, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(644, 4097, F64, 3, 3) (dual of [(4097, 3), 12287, 4]-NRT-code), using
- digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- digital (1, 4, 4097)-net over F64, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (19, 25, 2800298)-net over F64, using
(25, 31, large)-Net over F32 — Digital
Digital (25, 31, large)-net over F32, using
- t-expansion [i] based on digital (24, 31, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3231, large, F32, 7) (dual of [large, large−31, 8]-code), using
(25, 31, large)-Net in Base 32 — Upper bound on s
There is no (25, 31, large)-net in base 32, because
- 4 times m-reduction [i] would yield (25, 27, large)-net in base 32, but