Best Known (248−102, 248, s)-Nets in Base 3
(248−102, 248, 156)-Net over F3 — Constructive and digital
Digital (146, 248, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 124, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(248−102, 248, 209)-Net over F3 — Digital
Digital (146, 248, 209)-net over F3, using
(248−102, 248, 2024)-Net in Base 3 — Upper bound on s
There is no (146, 248, 2025)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21367 030182 922949 515115 972478 877610 408925 515858 881230 146834 860221 270755 605089 714920 989685 934400 010816 659742 181826 254139 > 3248 [i]