Best Known (129, 129+99, s)-Nets in Base 4
(129, 129+99, 130)-Net over F4 — Constructive and digital
Digital (129, 228, 130)-net over F4, using
- t-expansion [i] based on digital (105, 228, 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+99, 252)-Net over F4 — Digital
Digital (129, 228, 252)-net over F4, using
(129, 129+99, 3880)-Net in Base 4 — Upper bound on s
There is no (129, 228, 3881)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 227, 3881)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 47014 725092 341332 250567 133395 719832 062741 196598 729744 786199 562059 815738 178275 334283 055436 674513 485326 023992 241426 718897 165129 234686 639296 > 4227 [i]