Best Known (81−21, 81, s)-Nets in Base 32
(81−21, 81, 104857)-Net over F32 — Constructive and digital
Digital (60, 81, 104857)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 104857, F32, 21, 21) (dual of [(104857, 21), 2201916, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
(81−21, 81, 556314)-Net over F32 — Digital
Digital (60, 81, 556314)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3281, 556314, F32, 21) (dual of [556314, 556233, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
(81−21, 81, large)-Net in Base 32 — Upper bound on s
There is no (60, 81, large)-net in base 32, because
- 19 times m-reduction [i] would yield (60, 62, large)-net in base 32, but