Best Known (252−119, 252, s)-Nets in Base 4
(252−119, 252, 130)-Net over F4 — Constructive and digital
Digital (133, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(252−119, 252, 211)-Net over F4 — Digital
Digital (133, 252, 211)-net over F4, using
(252−119, 252, 2721)-Net in Base 4 — Upper bound on s
There is no (133, 252, 2722)-net in base 4, because
- 1 times m-reduction [i] would yield (133, 251, 2722)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 110181 402278 198610 900178 418937 817186 411963 761075 244112 401944 027276 309406 360443 511870 699924 264918 315314 635323 277232 979319 317742 103376 576624 673762 418240 > 4251 [i]