Best Known (129, 129+117, s)-Nets in Base 4
(129, 129+117, 130)-Net over F4 — Constructive and digital
Digital (129, 246, 130)-net over F4, using
- t-expansion [i] based on digital (105, 246, 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+117, 202)-Net over F4 — Digital
Digital (129, 246, 202)-net over F4, using
(129, 129+117, 2566)-Net in Base 4 — Upper bound on s
There is no (129, 246, 2567)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 245, 2567)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3239 083870 003750 284435 529671 871145 875161 676596 564743 130262 647484 280872 949655 727647 382163 791656 838777 315363 708946 604460 831134 582628 496354 175364 005952 > 4245 [i]