Best Known (42−9, 42, s)-Nets in Base 32
(42−9, 42, 2097150)-Net over F32 — Constructive and digital
Digital (33, 42, 2097150)-net over F32, using
- 321 times duplication [i] based on digital (32, 41, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F32, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(3241, 2097150, F32, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
(42−9, 42, large)-Net over F32 — Digital
Digital (33, 42, large)-net over F32, using
- 321 times duplication [i] based on digital (32, 41, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
(42−9, 42, large)-Net in Base 32 — Upper bound on s
There is no (33, 42, large)-net in base 32, because
- 7 times m-reduction [i] would yield (33, 35, large)-net in base 32, but