Best Known (52, 52+48, s)-Nets in Base 4
(52, 52+48, 66)-Net over F4 — Constructive and digital
Digital (52, 100, 66)-net over F4, using
- t-expansion [i] based on digital (49, 100, 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+48, 91)-Net over F4 — Digital
Digital (52, 100, 91)-net over F4, using
- t-expansion [i] based on digital (50, 100, 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+48, 1034)-Net in Base 4 — Upper bound on s
There is no (52, 100, 1035)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 621664 120961 821020 348483 464247 842219 677572 124332 101416 889664 > 4100 [i]