Best Known (68, 207, s)-Nets in Base 4
(68, 207, 66)-Net over F4 — Constructive and digital
Digital (68, 207, 66)-net over F4, using
- t-expansion [i] based on digital (49, 207, 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
(68, 207, 99)-Net over F4 — Digital
Digital (68, 207, 99)-net over F4, using
- t-expansion [i] based on digital (61, 207, 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
(68, 207, 499)-Net in Base 4 — Upper bound on s
There is no (68, 207, 500)-net in base 4, because
- 1 times m-reduction [i] would yield (68, 206, 500)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10906 945785 100414 934707 850718 378533 407596 053828 663894 724254 769251 344913 281243 622453 523262 899546 928901 628188 536612 163004 727036 > 4206 [i]