Best Known (247−121, 247, s)-Nets in Base 4
(247−121, 247, 130)-Net over F4 — Constructive and digital
Digital (126, 247, 130)-net over F4, using
- t-expansion [i] based on digital (105, 247, 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
(247−121, 247, 185)-Net over F4 — Digital
Digital (126, 247, 185)-net over F4, using
(247−121, 247, 2224)-Net in Base 4 — Upper bound on s
There is no (126, 247, 2225)-net in base 4, because
- 1 times m-reduction [i] would yield (126, 246, 2225)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13049 472364 229660 703051 721994 835081 554376 731144 362886 728784 070298 488336 649300 094067 907793 007148 277790 268824 941845 708584 510500 205666 127819 137676 246240 > 4246 [i]