Best Known (125, 125+98, s)-Nets in Base 4
(125, 125+98, 130)-Net over F4 — Constructive and digital
Digital (125, 223, 130)-net over F4, using
- t-expansion [i] based on digital (105, 223, 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+98, 238)-Net over F4 — Digital
Digital (125, 223, 238)-net over F4, using
(125, 125+98, 3460)-Net in Base 4 — Upper bound on s
There is no (125, 223, 3461)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 182 474349 766398 657561 946835 967426 382374 352083 884993 124009 380158 327757 322588 825300 323707 620451 444060 384032 085449 914136 303805 502758 908928 > 4223 [i]