Best Known (30, 41, s)-Nets in Base 32
(30, 41, 209715)-Net over F32 — Constructive and digital
Digital (30, 41, 209715)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 209715, F32, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
(30, 41, 654550)-Net over F32 — Digital
Digital (30, 41, 654550)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3241, 654550, F32, 11) (dual of [654550, 654509, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
(30, 41, large)-Net in Base 32 — Upper bound on s
There is no (30, 41, large)-net in base 32, because
- 9 times m-reduction [i] would yield (30, 32, large)-net in base 32, but