Best Known (89−23, 89, s)-Nets in Base 32
(89−23, 89, 95325)-Net over F32 — Constructive and digital
Digital (66, 89, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95325, F32, 23, 23) (dual of [(95325, 23), 2192386, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
(89−23, 89, 568091)-Net over F32 — Digital
Digital (66, 89, 568091)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3289, 568091, F32, 23) (dual of [568091, 568002, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using
(89−23, 89, large)-Net in Base 32 — Upper bound on s
There is no (66, 89, large)-net in base 32, because
- 21 times m-reduction [i] would yield (66, 68, large)-net in base 32, but