Best Known (249−103, 249, s)-Nets in Base 3
(249−103, 249, 148)-Net over F3 — Constructive and digital
Digital (146, 249, 148)-net over F3, using
- t-expansion [i] based on digital (142, 249, 148)-net over F3, using
- 1 times m-reduction [i] based on digital (142, 250, 148)-net over F3, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- trace code for nets [i] based on digital (17, 125, 74)-net over F9, using
- 1 times m-reduction [i] based on digital (142, 250, 148)-net over F3, using
(249−103, 249, 206)-Net over F3 — Digital
Digital (146, 249, 206)-net over F3, using
(249−103, 249, 2024)-Net in Base 3 — Upper bound on s
There is no (146, 249, 2025)-net in base 3, because
- 1 times m-reduction [i] would yield (146, 248, 2025)-net in base 3, but
- 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]