Best Known (67, 67+17, s)-Nets in Base 32
(67, 67+17, 1048575)-Net over F32 — Constructive and digital
Digital (67, 84, 1048575)-net over F32, using
- 323 times duplication [i] based on digital (64, 81, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
(67, 67+17, large)-Net over F32 — Digital
Digital (67, 84, large)-net over F32, using
- 323 times duplication [i] based on digital (64, 81, large)-net over F32, using
(67, 67+17, large)-Net in Base 32 — Upper bound on s
There is no (67, 84, large)-net in base 32, because
- 15 times m-reduction [i] would yield (67, 69, large)-net in base 32, but