Best Known (52, 52+70, s)-Nets in Base 4
(52, 52+70, 66)-Net over F4 — Constructive and digital
Digital (52, 122, 66)-net over F4, using
- t-expansion [i] based on digital (49, 122, 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
(52, 52+70, 91)-Net over F4 — Digital
Digital (52, 122, 91)-net over F4, using
- t-expansion [i] based on digital (50, 122, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(52, 52+70, 553)-Net in Base 4 — Upper bound on s
There is no (52, 122, 554)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 28 902255 523234 962282 930639 730281 168746 529913 454133 012463 286894 498809 166380 > 4122 [i]