Best Known (117, 117+88, s)-Nets in Base 4
(117, 117+88, 130)-Net over F4 — Constructive and digital
Digital (117, 205, 130)-net over F4, using
- t-expansion [i] based on digital (105, 205, 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
(117, 117+88, 238)-Net over F4 — Digital
Digital (117, 205, 238)-net over F4, using
(117, 117+88, 3635)-Net in Base 4 — Upper bound on s
There is no (117, 205, 3636)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2658 363827 248855 504458 870575 240269 532302 763349 391050 044533 624970 263248 765526 495043 656754 428958 192206 661043 271506 937586 809180 > 4205 [i]