Best Known (24, 24+9, s)-Nets in Base 32
(24, 24+9, 262144)-Net over F32 — Constructive and digital
Digital (24, 33, 262144)-net over F32, using
- net defined by OOA [i] based on linear OOA(3233, 262144, F32, 9, 9) (dual of [(262144, 9), 2359263, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using
(24, 24+9, 828402)-Net over F32 — Digital
Digital (24, 33, 828402)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3233, 828402, F32, 9) (dual of [828402, 828369, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3233, 1048576, F32, 9) (dual of [1048576, 1048543, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(3233, 1048576, F32, 9) (dual of [1048576, 1048543, 10]-code), using
(24, 24+9, large)-Net in Base 32 — Upper bound on s
There is no (24, 33, large)-net in base 32, because
- 7 times m-reduction [i] would yield (24, 26, large)-net in base 32, but