Best Known (46, 69, s)-Nets in Base 32
(46, 69, 2979)-Net over F32 — Constructive and digital
Digital (46, 69, 2979)-net over F32, using
- 322 times duplication [i] based on digital (44, 67, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3267, 32770, F32, 23) (dual of [32770, 32703, 24]-code), using
- net defined by OOA [i] based on linear OOA(3267, 2979, F32, 23, 23) (dual of [(2979, 23), 68450, 24]-NRT-code), using
(46, 69, 20929)-Net over F32 — Digital
Digital (46, 69, 20929)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3269, 20929, F32, 23) (dual of [20929, 20860, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3269, 32779, F32, 23) (dual of [32779, 32710, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3269, 32779, F32, 23) (dual of [32779, 32710, 24]-code), using
(46, 69, large)-Net in Base 32 — Upper bound on s
There is no (46, 69, large)-net in base 32, because
- 21 times m-reduction [i] would yield (46, 48, large)-net in base 32, but