Best Known (122, 243, s)-Nets in Base 4
(122, 243, 130)-Net over F4 — Constructive and digital
Digital (122, 243, 130)-net over F4, using
- t-expansion [i] based on digital (105, 243, 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
(122, 243, 173)-Net over F4 — Digital
Digital (122, 243, 173)-net over F4, using
(122, 243, 2023)-Net in Base 4 — Upper bound on s
There is no (122, 243, 2024)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 242, 2024)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 50 551818 633020 972186 660566 491019 413898 681004 748647 723726 199698 778488 125375 862732 140619 699223 910938 382089 208644 179135 342697 312774 074380 075482 499096 > 4242 [i]