Best Known (80, 127, s)-Nets in Base 5
(80, 127, 252)-Net over F5 — Constructive and digital
Digital (80, 127, 252)-net over F5, using
- 13 times m-reduction [i] based on digital (80, 140, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 70, 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
- trace code for nets [i] based on digital (10, 70, 126)-net over F25, using
(80, 127, 373)-Net over F5 — Digital
Digital (80, 127, 373)-net over F5, using
(80, 127, 15888)-Net in Base 5 — Upper bound on s
There is no (80, 127, 15889)-net in base 5, because
- 1 times m-reduction [i] would yield (80, 126, 15889)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 11765 946856 530711 430627 871107 040335 692817 552797 788930 348813 622449 894316 265226 960121 012525 > 5126 [i]