Best Known (55, 181, s)-Nets in Base 4
(55, 181, 66)-Net over F4 — Constructive and digital
Digital (55, 181, 66)-net over F4, using
- t-expansion [i] based on digital (49, 181, 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
(55, 181, 91)-Net over F4 — Digital
Digital (55, 181, 91)-net over F4, using
- t-expansion [i] based on digital (50, 181, 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
(55, 181, 385)-Net in Base 4 — Upper bound on s
There is no (55, 181, 386)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10 826301 502998 426922 105038 819685 416505 919635 459366 289523 942377 001027 437000 025901 645242 298934 890609 257257 947072 > 4181 [i]