Best Known (122, 122+92, s)-Nets in Base 4
(122, 122+92, 130)-Net over F4 — Constructive and digital
Digital (122, 214, 130)-net over F4, using
- t-expansion [i] based on digital (105, 214, 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
(122, 122+92, 246)-Net over F4 — Digital
Digital (122, 214, 246)-net over F4, using
(122, 122+92, 3755)-Net in Base 4 — Upper bound on s
There is no (122, 214, 3756)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 697 992367 835129 939796 622023 767455 534771 264152 638841 102132 942760 167154 352822 276067 584731 417114 089037 743682 556290 000631 588032 896544 > 4214 [i]