Best Known (53, 122, s)-Nets in Base 4
(53, 122, 66)-Net over F4 — Constructive and digital
Digital (53, 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
(53, 122, 91)-Net over F4 — Digital
Digital (53, 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
(53, 122, 599)-Net in Base 4 — Upper bound on s
There is no (53, 122, 600)-net in base 4, because
- 1 times m-reduction [i] would yield (53, 121, 600)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7 375062 368558 890642 169666 162151 374522 834289 067484 320779 837148 408608 262378 > 4121 [i]