Best Known (28, 38, s)-Nets in Base 32
(28, 38, 209717)-Net over F32 — Constructive and digital
Digital (28, 38, 209717)-net over F32, using
- net defined by OOA [i] based on linear OOA(3238, 209717, F32, 10, 10) (dual of [(209717, 10), 2097132, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3238, 1048585, F32, 10) (dual of [1048585, 1048547, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(3237, 1048576, F32, 10) (dual of [1048576, 1048539, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- OA 5-folding and stacking [i] based on linear OA(3238, 1048585, F32, 10) (dual of [1048585, 1048547, 11]-code), using
(28, 38, 1048585)-Net over F32 — Digital
Digital (28, 38, 1048585)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3238, 1048585, F32, 10) (dual of [1048585, 1048547, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(3237, 1048576, F32, 10) (dual of [1048576, 1048539, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
(28, 38, large)-Net in Base 32 — Upper bound on s
There is no (28, 38, large)-net in base 32, because
- 8 times m-reduction [i] would yield (28, 30, large)-net in base 32, but