Best Known (69, 69+22, s)-Nets in Base 32
(69, 69+22, 95328)-Net over F32 — Constructive and digital
Digital (69, 91, 95328)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 95328, F32, 22, 22) (dual of [(95328, 22), 2097125, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3291, 1048608, F32, 22) (dual of [1048608, 1048517, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, 1048609, F32, 22) (dual of [1048609, 1048518, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(21) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(3291, 1048609, F32, 22) (dual of [1048609, 1048518, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3291, 1048608, F32, 22) (dual of [1048608, 1048517, 23]-code), using
(69, 69+22, 190650)-Net in Base 32 — Constructive
(69, 91, 190650)-net in base 32, using
- base change [i] based on digital (43, 65, 190650)-net over F128, using
- 1281 times duplication [i] based on digital (42, 64, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- 1281 times duplication [i] based on digital (42, 64, 190650)-net over F128, using
(69, 69+22, 1048609)-Net over F32 — Digital
Digital (69, 91, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3291, 1048609, F32, 22) (dual of [1048609, 1048518, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(21) ⊂ Ce(14) [i] based on
(69, 69+22, large)-Net in Base 32 — Upper bound on s
There is no (69, 91, large)-net in base 32, because
- 20 times m-reduction [i] would yield (69, 71, large)-net in base 32, but