Best Known (68, 68+39, s)-Nets in Base 5
(68, 68+39, 252)-Net over F5 — Constructive and digital
Digital (68, 107, 252)-net over F5, using
- 9 times m-reduction [i] based on digital (68, 116, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 58, 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, 58, 126)-net over F25, using
(68, 68+39, 347)-Net over F5 — Digital
Digital (68, 107, 347)-net over F5, using
(68, 68+39, 15714)-Net in Base 5 — Upper bound on s
There is no (68, 107, 15715)-net in base 5, because
- 1 times m-reduction [i] would yield (68, 106, 15715)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 123 376633 265950 478684 133148 512374 428504 400514 344451 849429 713265 824615 581445 > 5106 [i]