Best Known (142−61, 142, s)-Nets in Base 5
(142−61, 142, 252)-Net over F5 — Constructive and digital
Digital (81, 142, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 71, 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
(142−61, 142, 5784)-Net in Base 5 — Upper bound on s
There is no (81, 142, 5785)-net in base 5, because
- 1 times m-reduction [i] would yield (81, 141, 5785)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 360 269566 411098 984612 128703 473804 112701 329432 004661 544817 694354 184816 540038 018363 811559 695444 935081 > 5141 [i]