Best Known (9, 9+10, s)-Nets in Base 32
(9, 9+10, 205)-Net over F32 — Constructive and digital
Digital (9, 19, 205)-net over F32, using
- net defined by OOA [i] based on linear OOA(3219, 205, F32, 10, 10) (dual of [(205, 10), 2031, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3219, 1025, F32, 10) (dual of [1025, 1006, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3219, 1026, F32, 10) (dual of [1026, 1007, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(3217, 1024, F32, 9) (dual of [1024, 1007, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3219, 1026, F32, 10) (dual of [1026, 1007, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3219, 1025, F32, 10) (dual of [1025, 1006, 11]-code), using
(9, 9+10, 258)-Net in Base 32 — Constructive
(9, 19, 258)-net in base 32, using
- 2 times m-reduction [i] based on (9, 21, 258)-net in base 32, using
- base change [i] based on (3, 15, 258)-net in base 128, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 14, 258)-net over F256, using
- 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
- base change [i] based on (3, 15, 258)-net in base 128, using
(9, 9+10, 490)-Net over F32 — Digital
Digital (9, 19, 490)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3219, 490, F32, 2, 10) (dual of [(490, 2), 961, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3219, 513, F32, 2, 10) (dual of [(513, 2), 1007, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3219, 1026, F32, 10) (dual of [1026, 1007, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(3217, 1024, F32, 9) (dual of [1024, 1007, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- OOA 2-folding [i] based on linear OA(3219, 1026, F32, 10) (dual of [1026, 1007, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(3219, 513, F32, 2, 10) (dual of [(513, 2), 1007, 11]-NRT-code), using
(9, 9+10, 44057)-Net in Base 32 — Upper bound on s
There is no (9, 19, 44058)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 39614 815243 544159 619649 548278 > 3219 [i]