Best Known (221−98, 221, s)-Nets in Base 4
(221−98, 221, 130)-Net over F4 — Constructive and digital
Digital (123, 221, 130)-net over F4, using
- t-expansion [i] based on digital (105, 221, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(221−98, 221, 229)-Net over F4 — Digital
Digital (123, 221, 229)-net over F4, using
(221−98, 221, 3268)-Net in Base 4 — Upper bound on s
There is no (123, 221, 3269)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11 505876 067508 018811 023736 799463 813842 661023 357988 981573 084338 815104 283683 330061 489197 753855 139222 151066 152460 937418 286066 586570 293504 > 4221 [i]