Best Known (126, 126+90, s)-Nets in Base 4
(126, 126+90, 130)-Net over F4 — Constructive and digital
Digital (126, 216, 130)-net over F4, using
- t-expansion [i] based on digital (105, 216, 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
(126, 126+90, 274)-Net over F4 — Digital
Digital (126, 216, 274)-net over F4, using
(126, 126+90, 4522)-Net in Base 4 — Upper bound on s
There is no (126, 216, 4523)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 11106 362597 078702 026458 368855 550777 344116 955268 448580 846180 736361 330283 736193 376340 434844 165245 624632 927135 252660 537171 188309 995584 > 4216 [i]