Best Known (9, 9+8, s)-Nets in Base 32
(9, 9+8, 258)-Net over F32 — Constructive and digital
Digital (9, 17, 258)-net over F32, using
- net defined by OOA [i] based on linear OOA(3217, 258, F32, 8, 8) (dual of [(258, 8), 2047, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3217, 1032, F32, 8) (dual of [1032, 1015, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(329, 1024, F32, 5) (dual of [1024, 1015, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- OA 4-folding and stacking [i] based on linear OA(3217, 1032, F32, 8) (dual of [1032, 1015, 9]-code), using
(9, 9+8, 259)-Net in Base 32 — Constructive
(9, 17, 259)-net in base 32, using
- 1 times m-reduction [i] based on (9, 18, 259)-net in base 32, using
- base change [i] based on (6, 15, 259)-net in base 64, using
- 1 times m-reduction [i] based on (6, 16, 259)-net in base 64, using
- base change [i] based on digital (2, 12, 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, 12, 259)-net over F256, using
- 1 times m-reduction [i] based on (6, 16, 259)-net in base 64, using
- base change [i] based on (6, 15, 259)-net in base 64, using
(9, 9+8, 995)-Net over F32 — Digital
Digital (9, 17, 995)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3217, 995, F32, 8) (dual of [995, 978, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3217, 1032, F32, 8) (dual of [1032, 1015, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(3215, 1024, F32, 8) (dual of [1024, 1009, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(329, 1024, F32, 5) (dual of [1024, 1015, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(3217, 1032, F32, 8) (dual of [1032, 1015, 9]-code), using
(9, 9+8, 178063)-Net in Base 32 — Upper bound on s
There is no (9, 17, 178064)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 38 686186 975537 572948 736437 > 3217 [i]