Best Known (23−12, 23, s)-Nets in Base 32
(23−12, 23, 171)-Net over F32 — Constructive and digital
Digital (11, 23, 171)-net over F32, using
- net defined by OOA [i] based on linear OOA(3223, 171, F32, 12, 12) (dual of [(171, 12), 2029, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
(23−12, 23, 259)-Net in Base 32 — Constructive
(11, 23, 259)-net in base 32, using
- 1 times m-reduction [i] based on (11, 24, 259)-net in base 32, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
(23−12, 23, 431)-Net over F32 — Digital
Digital (11, 23, 431)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3223, 431, F32, 2, 12) (dual of [(431, 2), 839, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 513, F32, 2, 12) (dual of [(513, 2), 1003, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(3223, 513, F32, 2, 12) (dual of [(513, 2), 1003, 13]-NRT-code), using
(23−12, 23, 56830)-Net in Base 32 — Upper bound on s
There is no (11, 23, 56831)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 41540 617899 068728 667871 245285 343431 > 3223 [i]