Best Known (20, 42, s)-Nets in Base 25
(20, 42, 148)-Net over F25 — Constructive and digital
Digital (20, 42, 148)-net over F25, using
- t-expansion [i] based on digital (19, 42, 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
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
(20, 42, 246)-Net over F25 — Digital
Digital (20, 42, 246)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2542, 246, F25, 22) (dual of [246, 204, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 312, F25, 22) (dual of [312, 270, 23]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2542, 312, F25, 22) (dual of [312, 270, 23]-code), using
(20, 42, 44497)-Net in Base 25 — Upper bound on s
There is no (20, 42, 44498)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 51701 041773 060767 561743 569102 801401 700581 662893 004478 630353 > 2542 [i]