Best Known (65, 65+35, s)-Nets in Base 32
(65, 65+35, 1927)-Net over F32 — Constructive and digital
Digital (65, 100, 1927)-net over F32, using
- net defined by OOA [i] based on linear OOA(32100, 1927, F32, 35, 35) (dual of [(1927, 35), 67345, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32100, 32760, F32, 35) (dual of [32760, 32660, 36]-code), using
(65, 65+35, 16385)-Net over F32 — Digital
Digital (65, 100, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(32100, 16385, F32, 2, 35) (dual of [(16385, 2), 32670, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32100, 32770, F32, 35) (dual of [32770, 32670, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32771, F32, 35) (dual of [32771, 32671, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(33) [i] based on
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3297, 32768, F32, 34) (dual of [32768, 32671, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(34) ⊂ Ce(33) [i] based on
- discarding factors / shortening the dual code based on linear OA(32100, 32771, F32, 35) (dual of [32771, 32671, 36]-code), using
- OOA 2-folding [i] based on linear OA(32100, 32770, F32, 35) (dual of [32770, 32670, 36]-code), using
(65, 65+35, large)-Net in Base 32 — Upper bound on s
There is no (65, 100, large)-net in base 32, because
- 33 times m-reduction [i] would yield (65, 67, large)-net in base 32, but