Best Known (129, 129+95, s)-Nets in Base 4
(129, 129+95, 130)-Net over F4 — Constructive and digital
Digital (129, 224, 130)-net over F4, using
- t-expansion [i] based on digital (105, 224, 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
(129, 129+95, 268)-Net over F4 — Digital
Digital (129, 224, 268)-net over F4, using
(129, 129+95, 4362)-Net in Base 4 — Upper bound on s
There is no (129, 224, 4363)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 223, 4363)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 182 573291 604603 032051 374819 200257 721325 702726 533773 583087 249631 131689 693989 642013 142393 146101 830480 877812 244472 174315 588720 602547 865088 > 4223 [i]