Best Known (242−59, 242, s)-Nets in Base 3
(242−59, 242, 400)-Net over F3 — Constructive and digital
Digital (183, 242, 400)-net over F3, using
- 32 times duplication [i] based on digital (181, 240, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 60, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 60, 100)-net over F81, using
(242−59, 242, 1099)-Net over F3 — Digital
Digital (183, 242, 1099)-net over F3, using
(242−59, 242, 53815)-Net in Base 3 — Upper bound on s
There is no (183, 242, 53816)-net in base 3, because
- 1 times m-reduction [i] would yield (183, 241, 53816)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 9 692340 992868 107785 256377 181945 389789 512462 229339 648653 570234 922511 141264 746248 762871 481010 368888 053600 549170 617457 > 3241 [i]