Best Known (139−41, 139, s)-Nets in Base 3
(139−41, 139, 204)-Net over F3 — Constructive and digital
Digital (98, 139, 204)-net over F3, using
- 31 times duplication [i] based on digital (97, 138, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 46, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- trace code for nets [i] based on digital (5, 46, 68)-net over F27, using
(139−41, 139, 345)-Net over F3 — Digital
Digital (98, 139, 345)-net over F3, using
(139−41, 139, 8116)-Net in Base 3 — Upper bound on s
There is no (98, 139, 8117)-net in base 3, because
- 1 times m-reduction [i] would yield (98, 138, 8117)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 696958 665043 280338 207315 137660 779328 433067 647680 996084 550425 145233 > 3138 [i]