Best Known (28−11, 28, s)-Nets in Base 64
(28−11, 28, 1638)-Net over F64 — Constructive and digital
Digital (17, 28, 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 (10, 21, 819)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 819, F64, 11, 11) (dual of [(819, 11), 8988, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(6421, 4096, F64, 11) (dual of [4096, 4075, 12]-code), using
- net defined by OOA [i] based on linear OOA(6421, 819, F64, 11, 11) (dual of [(819, 11), 8988, 12]-NRT-code), using
- digital (2, 7, 2016)-net over F64, using
(28−11, 28, 8207)-Net over F64 — Digital
Digital (17, 28, 8207)-net over F64, using
(28−11, 28, 13107)-Net in Base 64 — Constructive
(17, 28, 13107)-net in base 64, using
- base change [i] based on digital (10, 21, 13107)-net over F256, using
- net defined by OOA [i] based on linear OOA(25621, 13107, F256, 11, 11) (dual of [(13107, 11), 144156, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using
- net defined by OOA [i] based on linear OOA(25621, 13107, F256, 11, 11) (dual of [(13107, 11), 144156, 12]-NRT-code), using
(28−11, 28, 20651)-Net in Base 64
(17, 28, 20651)-net in base 64, using
- base change [i] based on digital (10, 21, 20651)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25621, 20651, F256, 3, 11) (dual of [(20651, 3), 61932, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25621, 21846, F256, 3, 11) (dual of [(21846, 3), 65517, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(25621, 65538, F256, 11) (dual of [65538, 65517, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(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(10) ⊂ Ce(9) [i] based on
- OOA 3-folding [i] based on linear OA(25621, 65538, F256, 11) (dual of [65538, 65517, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(25621, 21846, F256, 3, 11) (dual of [(21846, 3), 65517, 12]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25621, 20651, F256, 3, 11) (dual of [(20651, 3), 61932, 12]-NRT-code), using
(28−11, 28, large)-Net in Base 64 — Upper bound on s
There is no (17, 28, large)-net in base 64, because
- 9 times m-reduction [i] would yield (17, 19, large)-net in base 64, but