Best Known (14, 21, s)-Nets in Base 32
(14, 21, 10926)-Net over F32 — Constructive and digital
Digital (14, 21, 10926)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 10926, F32, 7, 7) (dual of [(10926, 7), 76461, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3221, 32779, F32, 7) (dual of [32779, 32758, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(3221, 32779, F32, 7) (dual of [32779, 32758, 8]-code), using
(14, 21, 21845)-Net in Base 32 — Constructive
(14, 21, 21845)-net in base 32, using
- net defined by OOA [i] based on OOA(3221, 21845, S32, 7, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(3221, 65536, S32, 7), using
- discarding factors based on OA(3221, 65538, S32, 7), using
- discarding parts of the base [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- discarding factors based on OA(3221, 65538, S32, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(3221, 65536, S32, 7), using
(14, 21, 32779)-Net over F32 — Digital
Digital (14, 21, 32779)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3221, 32779, F32, 7) (dual of [32779, 32758, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(6) ⊂ Ce(3) [i] based on
(14, 21, large)-Net in Base 32 — Upper bound on s
There is no (14, 21, large)-net in base 32, because
- 5 times m-reduction [i] would yield (14, 16, large)-net in base 32, but