Best Known (254−120, 254, s)-Nets in Base 4
(254−120, 254, 130)-Net over F4 — Constructive and digital
Digital (134, 254, 130)-net over F4, using
- t-expansion [i] based on digital (105, 254, 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
(254−120, 254, 212)-Net over F4 — Digital
Digital (134, 254, 212)-net over F4, using
(254−120, 254, 2685)-Net in Base 4 — Upper bound on s
There is no (134, 254, 2686)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 843 476757 126943 188434 019178 525776 189336 692636 269087 776312 586094 037724 230023 117570 408454 271544 213065 977271 438769 367636 282595 919386 929445 365388 036642 296439 > 4254 [i]