Best Known (226−97, 226, s)-Nets in Base 4
(226−97, 226, 130)-Net over F4 — Constructive and digital
Digital (129, 226, 130)-net over F4, using
- t-expansion [i] based on digital (105, 226, 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
(226−97, 226, 259)-Net over F4 — Digital
Digital (129, 226, 259)-net over F4, using
(226−97, 226, 4108)-Net in Base 4 — Upper bound on s
There is no (129, 226, 4109)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 225, 4109)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2923 911041 314743 754827 254506 914389 526562 765380 926537 690499 604325 257020 668893 217485 409689 894830 066859 225951 245698 025485 233373 397080 028928 > 4225 [i]