Best Known (234−54, 234, s)-Nets in Base 3
(234−54, 234, 600)-Net over F3 — Constructive and digital
Digital (180, 234, 600)-net over F3, using
- 32 times duplication [i] based on digital (178, 232, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 58, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 58, 150)-net over F81, using
(234−54, 234, 1342)-Net over F3 — Digital
Digital (180, 234, 1342)-net over F3, using
(234−54, 234, 74520)-Net in Base 3 — Upper bound on s
There is no (180, 234, 74521)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4431 183468 964872 953883 247237 997783 360482 368939 035210 669635 442595 399898 906065 378842 287855 641104 918230 840866 605787 > 3234 [i]