Best Known (125, 125+122, s)-Nets in Base 4
(125, 125+122, 130)-Net over F4 — Constructive and digital
Digital (125, 247, 130)-net over F4, using
- t-expansion [i] based on digital (105, 247, 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
(125, 125+122, 180)-Net over F4 — Digital
Digital (125, 247, 180)-net over F4, using
(125, 125+122, 2102)-Net in Base 4 — Upper bound on s
There is no (125, 247, 2103)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 51667 086814 666685 015615 406011 061459 039224 206914 821665 186204 327858 009961 976966 304651 552141 642050 856064 275282 618639 418049 697089 801495 794597 607091 571200 > 4247 [i]