Best Known (63, 63+43, s)-Nets in Base 5
(63, 63+43, 252)-Net over F5 — Constructive and digital
Digital (63, 106, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 53, 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
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(63, 63+43, 6765)-Net in Base 5 — Upper bound on s
There is no (63, 106, 6766)-net in base 5, because
- 1 times m-reduction [i] would yield (63, 105, 6766)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 24 683352 151550 715379 478260 559050 388377 484556 559925 098057 408390 854522 349625 > 5105 [i]