Best Known (38−20, 38, s)-Nets in Base 25
(38−20, 38, 132)-Net over F25 — Constructive and digital
Digital (18, 38, 132)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (4, 14, 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
- digital (4, 24, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25 (see above)
- digital (4, 14, 66)-net over F25, using
(38−20, 38, 228)-Net over F25 — Digital
Digital (18, 38, 228)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2538, 228, F25, 20) (dual of [228, 190, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2538, 312, F25, 20) (dual of [312, 274, 21]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2538, 312, F25, 20) (dual of [312, 274, 21]-code), using
(38−20, 38, 38715)-Net in Base 25 — Upper bound on s
There is no (18, 38, 38716)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 132374 906910 568428 120790 413582 198031 373822 275888 009153 > 2538 [i]