Best Known (83−20, 83, s)-Nets in Base 32
(83−20, 83, 104860)-Net over F32 — Constructive and digital
Digital (63, 83, 104860)-net over F32, using
- 322 times duplication [i] based on digital (61, 81, 104860)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 104860, F32, 20, 20) (dual of [(104860, 20), 2097119, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3281, 1048600, F32, 20) (dual of [1048600, 1048519, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- 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(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(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- OA 10-folding and stacking [i] based on linear OA(3281, 1048600, F32, 20) (dual of [1048600, 1048519, 21]-code), using
- net defined by OOA [i] based on linear OOA(3281, 104860, F32, 20, 20) (dual of [(104860, 20), 2097119, 21]-NRT-code), using
(83−20, 83, 209715)-Net in Base 32 — Constructive
(63, 83, 209715)-net in base 32, using
- 321 times duplication [i] based on (62, 82, 209715)-net in base 32, using
- net defined by OOA [i] based on OOA(3282, 209715, S32, 20, 20), using
- OA 10-folding and stacking [i] based on OA(3282, 2097150, S32, 20), using
- discarding factors based on OA(3282, 2097155, S32, 20), using
- discarding parts of the base [i] based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [i] based on
- discarding parts of the base [i] based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- discarding factors based on OA(3282, 2097155, S32, 20), using
- OA 10-folding and stacking [i] based on OA(3282, 2097150, S32, 20), using
- net defined by OOA [i] based on OOA(3282, 209715, S32, 20, 20), using
(83−20, 83, 1048609)-Net over F32 — Digital
Digital (63, 83, 1048609)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3283, 1048609, F32, 20) (dual of [1048609, 1048526, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- 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(3249, 1048576, F32, 13) (dual of [1048576, 1048527, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(19) ⊂ Ce(12) [i] based on
(83−20, 83, large)-Net in Base 32 — Upper bound on s
There is no (63, 83, large)-net in base 32, because
- 18 times m-reduction [i] would yield (63, 65, large)-net in base 32, but