Best Known (77, 122, s)-Nets in Base 5
(77, 122, 252)-Net over F5 — Constructive and digital
Digital (77, 122, 252)-net over F5, using
- 12 times m-reduction [i] based on digital (77, 134, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 67, 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, 67, 126)-net over F25, using
(77, 122, 366)-Net over F5 — Digital
Digital (77, 122, 366)-net over F5, using
(77, 122, 15801)-Net in Base 5 — Upper bound on s
There is no (77, 122, 15802)-net in base 5, because
- 1 times m-reduction [i] would yield (77, 121, 15802)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 3 766034 203372 756348 330870 949957 913634 912769 854863 668252 899449 611927 479783 069017 879425 > 5121 [i]