Best Known (125, 125+93, s)-Nets in Base 4
(125, 125+93, 130)-Net over F4 — Constructive and digital
Digital (125, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 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+93, 256)-Net over F4 — Digital
Digital (125, 218, 256)-net over F4, using
(125, 125+93, 4114)-Net in Base 4 — Upper bound on s
There is no (125, 218, 4115)-net in base 4, because
- 1 times m-reduction [i] would yield (125, 217, 4115)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 44691 326690 950959 261921 278981 328628 245433 555005 976358 725186 650222 074077 613657 506442 318339 629990 484470 142177 766464 963545 298512 539136 > 4217 [i]