Best Known (113, 113+106, s)-Nets in Base 4
(113, 113+106, 130)-Net over F4 — Constructive and digital
Digital (113, 219, 130)-net over F4, using
- t-expansion [i] based on digital (105, 219, 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
(113, 113+106, 172)-Net over F4 — Digital
Digital (113, 219, 172)-net over F4, using
(113, 113+106, 2067)-Net in Base 4 — Upper bound on s
There is no (113, 219, 2068)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 720977 868262 414843 112145 349314 363051 404474 920367 265762 831063 331852 637322 572363 390832 015231 167607 264827 390659 847283 365129 023693 780480 > 4219 [i]