Best Known (25, 25+17, s)-Nets in Base 4
(25, 25+17, 90)-Net over F4 — Constructive and digital
Digital (25, 42, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 21, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
(25, 25+17, 1521)-Net in Base 4 — Upper bound on s
There is no (25, 42, 1522)-net in base 4, because
- 1 times m-reduction [i] would yield (25, 41, 1522)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 4 839415 525402 571594 321818 > 441 [i]