Best Known (25−12, 25, s)-Nets in Base 32
(25−12, 25, 172)-Net over F32 — Constructive and digital
Digital (13, 25, 172)-net over F32, using
- net defined by OOA [i] based on linear OOA(3225, 172, F32, 12, 12) (dual of [(172, 12), 2039, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3225, 1032, F32, 12) (dual of [1032, 1007, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(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(11) ⊂ Ce(8) [i] based on
- OA 6-folding and stacking [i] based on linear OA(3225, 1032, F32, 12) (dual of [1032, 1007, 13]-code), using
(25−12, 25, 260)-Net in Base 32 — Constructive
(13, 25, 260)-net in base 32, using
- 321 times duplication [i] based on (12, 24, 260)-net in base 32, using
- base change [i] based on digital (3, 15, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 15, 260)-net over F256, using
(25−12, 25, 594)-Net over F32 — Digital
Digital (13, 25, 594)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3225, 594, F32, 12) (dual of [594, 569, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 1032, F32, 12) (dual of [1032, 1007, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(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(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 1032, F32, 12) (dual of [1032, 1007, 13]-code), using
(25−12, 25, 180431)-Net in Base 32 — Upper bound on s
There is no (13, 25, 180432)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 42 536127 042223 814882 208168 409718 520349 > 3225 [i]