Best Known (95−22, 95, s)-Nets in Base 32
(95−22, 95, 95329)-Net over F32 — Constructive and digital
Digital (73, 95, 95329)-net over F32, using
- 321 times duplication [i] based on digital (72, 94, 95329)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 95329, F32, 22, 22) (dual of [(95329, 22), 2097144, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3294, 1048619, F32, 22) (dual of [1048619, 1048525, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 1048620, F32, 22) (dual of [1048620, 1048526, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(12) [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(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(329, 44, F32, 8) (dual of [44, 35, 9]-code), using
- extended algebraic-geometric code AGe(F,35P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3294, 1048620, F32, 22) (dual of [1048620, 1048526, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3294, 1048619, F32, 22) (dual of [1048619, 1048525, 23]-code), using
- net defined by OOA [i] based on linear OOA(3294, 95329, F32, 22, 22) (dual of [(95329, 22), 2097144, 23]-NRT-code), using
(95−22, 95, 190651)-Net in Base 32 — Constructive
(73, 95, 190651)-net in base 32, using
- 322 times duplication [i] based on (71, 93, 190651)-net in base 32, using
- net defined by OOA [i] based on OOA(3293, 190651, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3293, 2097161, S32, 22), using
- discarding factors based on OA(3293, 2097163, S32, 22), using
- discarding parts of the base [i] based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] 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]
- 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(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- discarding parts of the base [i] based on linear OA(12866, 2097163, F128, 22) (dual of [2097163, 2097097, 23]-code), using
- discarding factors based on OA(3293, 2097163, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3293, 2097161, S32, 22), using
- net defined by OOA [i] based on OOA(3293, 190651, S32, 22, 22), using
(95−22, 95, 1803621)-Net over F32 — Digital
Digital (73, 95, 1803621)-net over F32, using
(95−22, 95, large)-Net in Base 32 — Upper bound on s
There is no (73, 95, large)-net in base 32, because
- 20 times m-reduction [i] would yield (73, 75, large)-net in base 32, but