Best Known (6, 10, s)-Nets in Base 32
(6, 10, 16385)-Net over F32 — Constructive and digital
Digital (6, 10, 16385)-net over F32, using
- net defined by OOA [i] based on linear OOA(3210, 16385, F32, 4, 4) (dual of [(16385, 4), 65530, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 32768, F32, 3) (dual of [32768, 32761, 4]-code or 32768-cap in PG(6,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(3210, 32770, F32, 4) (dual of [32770, 32760, 5]-code), using
(6, 10, 32640)-Net in Base 32 — Constructive
(6, 10, 32640)-net in base 32, using
- net defined by OOA [i] based on OOA(3210, 32640, S32, 4, 4), using
- OA 2-folding and stacking [i] based on OA(3210, 65280, S32, 4), using
- discarding parts of the base [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- discarding parts of the base [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- OA 2-folding and stacking [i] based on OA(3210, 65280, S32, 4), using
(6, 10, 32771)-Net over F32 — Digital
Digital (6, 10, 32771)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3210, 32771, F32, 4) (dual of [32771, 32761, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 32768, F32, 3) (dual of [32768, 32761, 4]-code or 32768-cap in PG(6,32)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(3) ⊂ Ce(2) [i] based on
(6, 10, 1530745)-Net in Base 32 — Upper bound on s
There is no (6, 10, 1530746)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1125 900414 015644 > 3210 [i]