Best Known (138, 138+112, s)-Nets in Base 4
(138, 138+112, 130)-Net over F4 — Constructive and digital
Digital (138, 250, 130)-net over F4, using
- t-expansion [i] based on digital (105, 250, 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
(138, 138+112, 248)-Net over F4 — Digital
Digital (138, 250, 248)-net over F4, using
(138, 138+112, 3480)-Net in Base 4 — Upper bound on s
There is no (138, 250, 3481)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 320429 122932 773738 327311 140434 065969 127985 087606 837459 456416 718539 054326 955709 929529 068031 690999 263993 919482 264412 209223 633104 796920 583650 336481 306748 > 4250 [i]