Best Known (79, 79+59, s)-Nets in Base 5
(79, 79+59, 252)-Net over F5 — Constructive and digital
Digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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
(79, 79+59, 5827)-Net in Base 5 — Upper bound on s
There is no (79, 138, 5828)-net in base 5, because
- 1 times m-reduction [i] would yield (79, 137, 5828)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 574178 300076 852409 539254 369588 500099 747212 432279 561779 798553 706309 066150 893731 016360 642007 348625 > 5137 [i]