Best Known (10, 21, s)-Nets in Base 32
(10, 21, 205)-Net over F32 — Constructive and digital
Digital (10, 21, 205)-net over F32, using
- net defined by OOA [i] based on linear OOA(3221, 205, F32, 11, 11) (dual of [(205, 11), 2234, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3221, 1026, F32, 11) (dual of [1026, 1005, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3219, 1024, F32, 10) (dual of [1024, 1005, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(3221, 1026, F32, 11) (dual of [1026, 1005, 12]-code), using
(10, 21, 259)-Net in Base 32 — Constructive
(10, 21, 259)-net in base 32, using
- base change [i] based on (4, 15, 259)-net in base 128, using
- 1 times m-reduction [i] based on (4, 16, 259)-net in base 128, using
- base change [i] based on digital (2, 14, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 14, 259)-net over F256, using
- 1 times m-reduction [i] based on (4, 16, 259)-net in base 128, using
(10, 21, 453)-Net over F32 — Digital
Digital (10, 21, 453)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3221, 453, F32, 2, 11) (dual of [(453, 2), 885, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3221, 513, F32, 2, 11) (dual of [(513, 2), 1005, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3221, 1026, F32, 11) (dual of [1026, 1005, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3219, 1024, F32, 10) (dual of [1024, 1005, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(3221, 1026, F32, 11) (dual of [1026, 1005, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(3221, 513, F32, 2, 11) (dual of [(513, 2), 1005, 12]-NRT-code), using
(10, 21, 88117)-Net in Base 32 — Upper bound on s
There is no (10, 21, 88118)-net in base 32, because
- 1 times m-reduction [i] would yield (10, 20, 88118)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 1 267662 489714 718757 483392 191755 > 3220 [i]