Best Known (15, 29, s)-Nets in Base 32
(15, 29, 147)-Net over F32 — Constructive and digital
Digital (15, 29, 147)-net over F32, using
- 1 times m-reduction [i] based on digital (15, 30, 147)-net over F32, using
- net defined by OOA [i] based on linear OOA(3230, 147, F32, 15, 15) (dual of [(147, 15), 2175, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3230, 1030, F32, 15) (dual of [1030, 1000, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3229, 1025, F32, 15) (dual of [1025, 996, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3225, 1025, F32, 13) (dual of [1025, 1000, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(3230, 1030, F32, 15) (dual of [1030, 1000, 16]-code), using
- net defined by OOA [i] based on linear OOA(3230, 147, F32, 15, 15) (dual of [(147, 15), 2175, 16]-NRT-code), using
(15, 29, 260)-Net in Base 32 — Constructive
(15, 29, 260)-net in base 32, using
- 3 times m-reduction [i] based on (15, 32, 260)-net in base 32, using
- base change [i] based on digital (3, 20, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 20, 260)-net over F256, using
(15, 29, 549)-Net over F32 — Digital
Digital (15, 29, 549)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3229, 549, F32, 14) (dual of [549, 520, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3229, 1032, F32, 14) (dual of [1032, 1003, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(3227, 1024, F32, 14) (dual of [1024, 997, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3229, 1032, F32, 14) (dual of [1032, 1003, 15]-code), using
(15, 29, 187573)-Net in Base 32 — Upper bound on s
There is no (15, 29, 187574)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 44 602795 569722 765998 002678 385259 251880 157144 > 3229 [i]