Best Known (16, 16+10, s)-Nets in Base 64
(16, 16+10, 1638)-Net over F64 — Constructive and digital
Digital (16, 26, 1638)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 2016)-net over F64, using
- net defined by OOA [i] based on linear OOA(647, 2016, F64, 5, 5) (dual of [(2016, 5), 10073, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- net defined by OOA [i] based on linear OOA(647, 2016, F64, 5, 5) (dual of [(2016, 5), 10073, 6]-NRT-code), using
- digital (9, 19, 819)-net over F64, using
- net defined by OOA [i] based on linear OOA(6419, 819, F64, 10, 10) (dual of [(819, 10), 8171, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6419, 4095, F64, 10) (dual of [4095, 4076, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6419, 4095, F64, 10) (dual of [4095, 4076, 11]-code), using
- net defined by OOA [i] based on linear OOA(6419, 819, F64, 10, 10) (dual of [(819, 10), 8171, 11]-NRT-code), using
- digital (2, 7, 2016)-net over F64, using
(16, 16+10, 10875)-Net over F64 — Digital
Digital (16, 26, 10875)-net over F64, using
(16, 16+10, 13107)-Net in Base 64 — Constructive
(16, 26, 13107)-net in base 64, using
- net defined by OOA [i] based on OOA(6426, 13107, S64, 10, 10), using
- OA 5-folding and stacking [i] based on OA(6426, 65535, S64, 10), using
- discarding factors based on OA(6426, 65538, S64, 10), using
- discarding parts of the base [i] based on linear OA(25619, 65538, F256, 10) (dual of [65538, 65519, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding parts of the base [i] based on linear OA(25619, 65538, F256, 10) (dual of [65538, 65519, 11]-code), using
- discarding factors based on OA(6426, 65538, S64, 10), using
- OA 5-folding and stacking [i] based on OA(6426, 65535, S64, 10), using
(16, 16+10, large)-Net in Base 64 — Upper bound on s
There is no (16, 26, large)-net in base 64, because
- 8 times m-reduction [i] would yield (16, 18, large)-net in base 64, but