Best Known (72, 72+23, s)-Nets in Base 32
(72, 72+23, 95328)-Net over F32 — Constructive and digital
Digital (72, 95, 95328)-net over F32, using
- net defined by OOA [i] based on linear OOA(3295, 95328, F32, 23, 23) (dual of [(95328, 23), 2192449, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3295, 1048609, F32, 23) (dual of [1048609, 1048514, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [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(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(22) ⊂ Ce(15) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(3295, 1048609, F32, 23) (dual of [1048609, 1048514, 24]-code), using
(72, 72+23, 190650)-Net in Base 32 — Constructive
(72, 95, 190650)-net in base 32, using
- 321 times duplication [i] based on (71, 94, 190650)-net in base 32, using
- net defined by OOA [i] based on OOA(3294, 190650, S32, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(3294, 2097151, S32, 23), using
- discarding factors based on OA(3294, 2097155, S32, 23), using
- discarding parts of the base [i] based on linear OA(12867, 2097155, F128, 23) (dual of [2097155, 2097088, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(12867, 2097155, F128, 23) (dual of [2097155, 2097088, 24]-code), using
- discarding factors based on OA(3294, 2097155, S32, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(3294, 2097151, S32, 23), using
- net defined by OOA [i] based on OOA(3294, 190650, S32, 23, 23), using
(72, 72+23, 1048609)-Net over F32 — Digital
Digital (72, 95, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3295, 1048609, F32, 23) (dual of [1048609, 1048514, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [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(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(22) ⊂ Ce(15) [i] based on
(72, 72+23, large)-Net in Base 32 — Upper bound on s
There is no (72, 95, large)-net in base 32, because
- 21 times m-reduction [i] would yield (72, 74, large)-net in base 32, but