Best Known (203−142, 203, s)-Nets in Base 4
(203−142, 203, 66)-Net over F4 — Constructive and digital
Digital (61, 203, 66)-net over F4, using
- t-expansion [i] based on digital (49, 203, 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
(203−142, 203, 99)-Net over F4 — Digital
Digital (61, 203, 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
(203−142, 203, 422)-Net in Base 4 — Upper bound on s
There is no (61, 203, 423)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 180 072822 918052 380065 928740 694544 181231 981959 670898 810996 602926 462653 519306 862300 844734 031173 443450 222746 639485 823095 445800 > 4203 [i]