Best Known (69, 92, s)-Nets in Base 32
(69, 92, 95326)-Net over F32 — Constructive and digital
Digital (69, 92, 95326)-net over F32, using
- 321 times duplication [i] based on digital (68, 91, 95326)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 95326, F32, 23, 23) (dual of [(95326, 23), 2192407, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3291, 1048587, F32, 23) (dual of [1048587, 1048496, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, 1048590, F32, 23) (dual of [1048590, 1048499, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(3289, 1048576, F32, 23) (dual of [1048576, 1048487, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-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(3291, 1048590, F32, 23) (dual of [1048590, 1048499, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3291, 1048587, F32, 23) (dual of [1048587, 1048496, 24]-code), using
- net defined by OOA [i] based on linear OOA(3291, 95326, F32, 23, 23) (dual of [(95326, 23), 2192407, 24]-NRT-code), using
(69, 92, 932057)-Net over F32 — Digital
Digital (69, 92, 932057)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3292, 932057, F32, 23) (dual of [932057, 931965, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3292, 1048596, F32, 23) (dual of [1048596, 1048504, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(3289, 1048577, F32, 23) (dual of [1048577, 1048488, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(3273, 1048577, F32, 19) (dual of [1048577, 1048504, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3292, 1048596, F32, 23) (dual of [1048596, 1048504, 24]-code), using
(69, 92, large)-Net in Base 32 — Upper bound on s
There is no (69, 92, large)-net in base 32, because
- 21 times m-reduction [i] would yield (69, 71, large)-net in base 32, but