Best Known (108−34, 108, s)-Nets in Base 32
(108−34, 108, 1929)-Net over F32 — Constructive and digital
Digital (74, 108, 1929)-net over F32, using
- 321 times duplication [i] based on digital (73, 107, 1929)-net over F32, using
- t-expansion [i] based on digital (72, 107, 1929)-net over F32, using
- net defined by OOA [i] based on linear OOA(32107, 1929, F32, 35, 35) (dual of [(1929, 35), 67408, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32107, 32794, F32, 35) (dual of [32794, 32687, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(32107, 32796, F32, 35) (dual of [32796, 32689, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(26) [i] based on
- linear OA(32100, 32768, F32, 35) (dual of [32768, 32668, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(327, 28, F32, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,32)), using
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- discarding factors / shortening the dual code based on linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- construction X applied to Ce(34) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(32107, 32796, F32, 35) (dual of [32796, 32689, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(32107, 32794, F32, 35) (dual of [32794, 32687, 36]-code), using
- net defined by OOA [i] based on linear OOA(32107, 1929, F32, 35, 35) (dual of [(1929, 35), 67408, 36]-NRT-code), using
- t-expansion [i] based on digital (72, 107, 1929)-net over F32, using
(108−34, 108, 3855)-Net in Base 32 — Constructive
(74, 108, 3855)-net in base 32, using
- net defined by OOA [i] based on OOA(32108, 3855, S32, 34, 34), using
- OA 17-folding and stacking [i] based on OA(32108, 65535, S32, 34), using
- discarding factors based on OA(32108, 65538, S32, 34), using
- discarding parts of the base [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(25667, 65536, F256, 34) (dual of [65536, 65469, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(25665, 65536, F256, 33) (dual of [65536, 65471, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(33) ⊂ Ce(32) [i] based on
- discarding parts of the base [i] based on linear OA(25667, 65538, F256, 34) (dual of [65538, 65471, 35]-code), using
- discarding factors based on OA(32108, 65538, S32, 34), using
- OA 17-folding and stacking [i] based on OA(32108, 65535, S32, 34), using
(108−34, 108, 35821)-Net over F32 — Digital
Digital (74, 108, 35821)-net over F32, using
(108−34, 108, large)-Net in Base 32 — Upper bound on s
There is no (74, 108, large)-net in base 32, because
- 32 times m-reduction [i] would yield (74, 76, large)-net in base 32, but