Best Known (129, 129+105, s)-Nets in Base 4
(129, 129+105, 130)-Net over F4 — Constructive and digital
Digital (129, 234, 130)-net over F4, using
- t-expansion [i] based on digital (105, 234, 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+105, 232)-Net over F4 — Digital
Digital (129, 234, 232)-net over F4, using
(129, 129+105, 3318)-Net in Base 4 — Upper bound on s
There is no (129, 234, 3319)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 233, 3319)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 192 408832 318853 033319 057542 590243 824483 984107 388047 423811 164642 699718 210752 957302 264666 679081 974928 775599 733390 411279 521604 058947 164727 715225 > 4233 [i]