Best Known (14, 29, s)-Nets in Base 32
(14, 29, 146)-Net over F32 — Constructive and digital
Digital (14, 29, 146)-net over F32, using
- net defined by OOA [i] based on linear OOA(3229, 146, F32, 15, 15) (dual of [(146, 15), 2161, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(3229, 1023, F32, 15) (dual of [1023, 994, 16]-code), using
(14, 29, 259)-Net in Base 32 — Constructive
(14, 29, 259)-net in base 32, using
- 3 times m-reduction [i] based on (14, 32, 259)-net in base 32, using
- base change [i] based on digital (2, 20, 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, 20, 259)-net over F256, using
(14, 29, 410)-Net over F32 — Digital
Digital (14, 29, 410)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3229, 410, F32, 2, 15) (dual of [(410, 2), 791, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3229, 513, F32, 2, 15) (dual of [(513, 2), 997, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3229, 1026, F32, 15) (dual of [1026, 997, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(3229, 1024, F32, 15) (dual of [1024, 995, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 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(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(14) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(3229, 1026, F32, 15) (dual of [1026, 997, 16]-code), using
- discarding factors / shortening the dual code based on linear OOA(3229, 513, F32, 2, 15) (dual of [(513, 2), 997, 16]-NRT-code), using
(14, 29, 114325)-Net in Base 32 — Upper bound on s
There is no (14, 29, 114326)-net in base 32, because
- 1 times m-reduction [i] would yield (14, 28, 114326)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 393805 449374 956868 998147 733209 890606 827528 > 3228 [i]