Best Known (41−22, 41, s)-Nets in Base 25
(41−22, 41, 148)-Net over F25 — Constructive and digital
Digital (19, 41, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(41−22, 41, 208)-Net over F25 — Digital
Digital (19, 41, 208)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2541, 208, F25, 22) (dual of [208, 167, 23]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 208 | 252−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
(41−22, 41, 33207)-Net in Base 25 — Upper bound on s
There is no (19, 41, 33208)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2068 345061 626985 877631 920782 512294 280982 226429 961321 006785 > 2541 [i]