Best Known (126, 126+108, s)-Nets in Base 4
(126, 126+108, 130)-Net over F4 — Constructive and digital
Digital (126, 234, 130)-net over F4, using
- t-expansion [i] based on digital (105, 234, 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+108, 213)-Net over F4 — Digital
Digital (126, 234, 213)-net over F4, using
(126, 126+108, 2795)-Net in Base 4 — Upper bound on s
There is no (126, 234, 2796)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 762 720048 952311 304787 461454 249715 001151 614979 670131 877328 360908 964506 943541 654980 693324 623925 310952 505289 846666 964638 905174 283493 478237 344280 > 4234 [i]