Best Known (69, 93, s)-Nets in Base 32
(69, 93, 87381)-Net over F32 — Constructive and digital
Digital (69, 93, 87381)-net over F32, using
- net defined by OOA [i] based on linear OOA(3293, 87381, F32, 24, 24) (dual of [(87381, 24), 2097051, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3293, 1048572, F32, 24) (dual of [1048572, 1048479, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3293, 1048572, F32, 24) (dual of [1048572, 1048479, 25]-code), using
(69, 93, 575105)-Net over F32 — Digital
Digital (69, 93, 575105)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3293, 575105, F32, 24) (dual of [575105, 575012, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(3293, 1048576, F32, 24) (dual of [1048576, 1048483, 25]-code), using
(69, 93, large)-Net in Base 32 — Upper bound on s
There is no (69, 93, large)-net in base 32, because
- 22 times m-reduction [i] would yield (69, 71, large)-net in base 32, but