Best Known (123, 123+38, s)-Nets in Base 3
(123, 123+38, 464)-Net over F3 — Constructive and digital
Digital (123, 161, 464)-net over F3, using
- 31 times duplication [i] based on digital (122, 160, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 40, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 40, 116)-net over F81, using
(123, 123+38, 891)-Net over F3 — Digital
Digital (123, 161, 891)-net over F3, using
(123, 123+38, 43749)-Net in Base 3 — Upper bound on s
There is no (123, 161, 43750)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 65546 012693 578387 409215 097891 674577 322142 379735 246412 416735 600236 533017 720001 > 3161 [i]