Best Known (69, 69+36, s)-Nets in Base 32
(69, 69+36, 1821)-Net over F32 — Constructive and digital
Digital (69, 105, 1821)-net over F32, using
- net defined by OOA [i] based on linear OOA(32105, 1821, F32, 36, 36) (dual of [(1821, 36), 65451, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(32105, 32778, F32, 36) (dual of [32778, 32673, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32105, 32779, F32, 36) (dual of [32779, 32674, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(35) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(32105, 32779, F32, 36) (dual of [32779, 32674, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(32105, 32778, F32, 36) (dual of [32778, 32673, 37]-code), using
(69, 69+36, 17526)-Net over F32 — Digital
Digital (69, 105, 17526)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32105, 17526, F32, 36) (dual of [17526, 17421, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(32105, 32779, F32, 36) (dual of [32779, 32674, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- linear OA(32103, 32768, F32, 36) (dual of [32768, 32665, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(35) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(32105, 32779, F32, 36) (dual of [32779, 32674, 37]-code), using
(69, 69+36, large)-Net in Base 32 — Upper bound on s
There is no (69, 105, large)-net in base 32, because
- 34 times m-reduction [i] would yield (69, 71, large)-net in base 32, but