Best Known (22, 32, s)-Nets in Base 5
(22, 32, 132)-Net over F5 — Constructive and digital
Digital (22, 32, 132)-net over F5, using
- 4 times m-reduction [i] based on digital (22, 36, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 18, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 18, 66)-net over F25, using
(22, 32, 476)-Net over F5 — Digital
Digital (22, 32, 476)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(532, 476, F5, 10) (dual of [476, 444, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(532, 624, F5, 10) (dual of [624, 592, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(532, 624, F5, 10) (dual of [624, 592, 11]-code), using
(22, 32, 19369)-Net in Base 5 — Upper bound on s
There is no (22, 32, 19370)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 23287 941462 367417 655977 > 532 [i]