Best Known (239−119, 239, s)-Nets in Base 4
(239−119, 239, 130)-Net over F4 — Constructive and digital
Digital (120, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(239−119, 239, 171)-Net over F4 — Digital
Digital (120, 239, 171)-net over F4, using
(239−119, 239, 1992)-Net in Base 4 — Upper bound on s
There is no (120, 239, 1993)-net in base 4, because
- 1 times m-reduction [i] would yield (120, 238, 1993)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 195766 871957 355615 912174 128968 759135 666122 481913 191500 258483 719994 045005 570992 330327 011415 179889 158876 530923 165582 799115 946496 902389 450471 531328 > 4238 [i]