Best Known (81, 81+20, s)-Nets in Base 32
(81, 81+20, 838860)-Net over F32 — Constructive and digital
Digital (81, 101, 838860)-net over F32, using
- t-expansion [i] based on digital (80, 101, 838860)-net over F32, using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(32101, large, F32, 21) (dual of [large, large−101, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(32101, 8388601, F32, 21) (dual of [8388601, 8388500, 22]-code), using
- net defined by OOA [i] based on linear OOA(32101, 838860, F32, 21, 21) (dual of [(838860, 21), 17615959, 22]-NRT-code), using
(81, 81+20, large)-Net over F32 — Digital
Digital (81, 101, large)-net over F32, using
- 321 times duplication [i] based on digital (80, 100, large)-net over F32, using
- t-expansion [i] based on digital (79, 100, large)-net over F32, using
(81, 81+20, large)-Net in Base 32 — Upper bound on s
There is no (81, 101, large)-net in base 32, because
- 18 times m-reduction [i] would yield (81, 83, large)-net in base 32, but