Best Known (15, 21, s)-Nets in Base 32
(15, 21, 349526)-Net over F32 — Constructive and digital
Digital (15, 21, 349526)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(3221, 1048578, F32, 6) (dual of [1048578, 1048557, 7]-code), using
(15, 21, 1048580)-Net over F32 — Digital
Digital (15, 21, 1048580)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
(15, 21, large)-Net in Base 32 — Upper bound on s
There is no (15, 21, large)-net in base 32, because
- 4 times m-reduction [i] would yield (15, 17, large)-net in base 32, but