Best Known (71, 71+22, s)-Nets in Base 32
(71, 71+22, 95328)-Net over F32 — Constructive and digital
Digital (71, 93, 95328)-net over F32, using
- 322 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(3291, 95328, F32, 22, 22) (dual of [(95328, 22), 2097125, 23]-NRT-code), using
(71, 71+22, 190651)-Net in Base 32 — Constructive
(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
(71, 71+22, 1296578)-Net over F32 — Digital
Digital (71, 93, 1296578)-net over F32, using
(71, 71+22, large)-Net in Base 32 — Upper bound on s
There is no (71, 93, large)-net in base 32, because
- 20 times m-reduction [i] would yield (71, 73, large)-net in base 32, but