Best Known (45, 59, s)-Nets in Base 32
(45, 59, 149801)-Net over F32 — Constructive and digital
Digital (45, 59, 149801)-net over F32, using
- net defined by OOA [i] based on linear OOA(3259, 149801, F32, 14, 14) (dual of [(149801, 14), 2097155, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3259, 1048607, F32, 14) (dual of [1048607, 1048548, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3259, 1048609, F32, 14) (dual of [1048609, 1048550, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
- linear OA(3253, 1048576, F32, 14) (dual of [1048576, 1048523, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(13) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(3259, 1048609, F32, 14) (dual of [1048609, 1048550, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3259, 1048607, F32, 14) (dual of [1048607, 1048548, 15]-code), using
(45, 59, 299594)-Net in Base 32 — Constructive
(45, 59, 299594)-net in base 32, using
- 321 times duplication [i] based on (44, 58, 299594)-net in base 32, using
- net defined by OOA [i] based on OOA(3258, 299594, S32, 14, 14), using
- OA 7-folding and stacking [i] based on OA(3258, 2097158, S32, 14), using
- discarding factors based on OA(3258, 2097159, S32, 14), using
- discarding parts of the base [i] based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(12841, 2097159, F128, 14) (dual of [2097159, 2097118, 15]-code), using
- discarding factors based on OA(3258, 2097159, S32, 14), using
- OA 7-folding and stacking [i] based on OA(3258, 2097158, S32, 14), using
- net defined by OOA [i] based on OOA(3258, 299594, S32, 14, 14), using
(45, 59, 1239116)-Net over F32 — Digital
Digital (45, 59, 1239116)-net over F32, using
(45, 59, large)-Net in Base 32 — Upper bound on s
There is no (45, 59, large)-net in base 32, because
- 12 times m-reduction [i] would yield (45, 47, large)-net in base 32, but