Best Known (24, 24+25, s)-Nets in Base 25
(24, 24+25, 156)-Net over F25 — Constructive and digital
Digital (24, 49, 156)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- digital (9, 34, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (3, 15, 52)-net over F25, using
(24, 24+25, 315)-Net over F25 — Digital
Digital (24, 49, 315)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2549, 315, F25, 25) (dual of [315, 266, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2549, 624, F25, 25) (dual of [624, 575, 26]-code), using
(24, 24+25, 86075)-Net in Base 25 — Upper bound on s
There is no (24, 49, 86076)-net in base 25, because
- 1 times m-reduction [i] would yield (24, 48, 86076)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 12 622521 367198 463930 693447 107032 294595 552210 354208 651783 336649 105025 > 2548 [i]