Best Known (10, 63, s)-Nets in Base 25
(10, 63, 126)-Net over F25 — Constructive and digital
Digital (10, 63, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
(10, 63, 934)-Net in Base 25 — Upper bound on s
There is no (10, 63, 935)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 62, 935)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 482 289269 487180 828964 032062 825644 921287 131392 326389 773306 059991 303919 217673 519941 664273 > 2562 [i]