Best Known (204−138, 204, s)-Nets in Base 4
(204−138, 204, 66)-Net over F4 — Constructive and digital
Digital (66, 204, 66)-net over F4, using
- t-expansion [i] based on digital (49, 204, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(204−138, 204, 99)-Net over F4 — Digital
Digital (66, 204, 99)-net over F4, using
- t-expansion [i] based on digital (61, 204, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(204−138, 204, 477)-Net in Base 4 — Upper bound on s
There is no (66, 204, 478)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 661 760900 311967 189319 698346 675748 584719 797053 555435 915068 922191 328253 500905 852943 256613 025720 508010 900992 625295 659944 628659 > 4204 [i]