Best Known (245−122, 245, s)-Nets in Base 4
(245−122, 245, 130)-Net over F4 — Constructive and digital
Digital (123, 245, 130)-net over F4, using
- t-expansion [i] based on digital (105, 245, 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
(245−122, 245, 174)-Net over F4 — Digital
Digital (123, 245, 174)-net over F4, using
(245−122, 245, 2007)-Net in Base 4 — Upper bound on s
There is no (123, 245, 2008)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3291 335862 757817 852424 661706 714800 126399 315080 180801 704185 029755 722715 327756 517676 473747 176127 381132 752708 479347 999042 203049 221946 486689 649745 460920 > 4245 [i]