Best Known (13−5, 13, s)-Nets in Base 32
(13−5, 13, 16385)-Net over F32 — Constructive and digital
Digital (8, 13, 16385)-net over F32, using
- net defined by OOA [i] based on linear OOA(3213, 16385, F32, 5, 5) (dual of [(16385, 5), 81912, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3213, 32771, F32, 5) (dual of [32771, 32758, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(3213, 32768, F32, 5) (dual of [32768, 32755, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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(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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(3213, 32771, F32, 5) (dual of [32771, 32758, 6]-code), using
(13−5, 13, 32640)-Net in Base 32 — Constructive
(8, 13, 32640)-net in base 32, using
- 321 times duplication [i] based on (7, 12, 32640)-net in base 32, using
- net defined by OOA [i] based on OOA(3212, 32640, S32, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(3212, 65281, S32, 5), using
- discarding parts of the base [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(3212, 65281, S32, 5), using
- net defined by OOA [i] based on OOA(3212, 32640, S32, 5, 5), using
(13−5, 13, 32771)-Net over F32 — Digital
Digital (8, 13, 32771)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3213, 32771, F32, 5) (dual of [32771, 32758, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(3213, 32768, F32, 5) (dual of [32768, 32755, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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(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(4) ⊂ Ce(3) [i] based on
(13−5, 13, large)-Net in Base 32 — Upper bound on s
There is no (8, 13, large)-net in base 32, because
- 3 times m-reduction [i] would yield (8, 10, large)-net in base 32, but