Best Known (109, 109+72, s)-Nets in Base 4
(109, 109+72, 130)-Net over F4 — Constructive and digital
Digital (109, 181, 130)-net over F4, using
- t-expansion [i] based on digital (105, 181, 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
(109, 109+72, 273)-Net over F4 — Digital
Digital (109, 181, 273)-net over F4, using
(109, 109+72, 5036)-Net in Base 4 — Upper bound on s
There is no (109, 181, 5037)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 443151 016964 176366 221872 587718 747214 935706 320410 155466 905480 323357 717349 313010 487526 139681 209068 925400 723167 > 4181 [i]