Best Known (138−83, 138, s)-Nets in Base 4
(138−83, 138, 66)-Net over F4 — Constructive and digital
Digital (55, 138, 66)-net over F4, using
- t-expansion [i] based on digital (49, 138, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(138−83, 138, 91)-Net over F4 — Digital
Digital (55, 138, 91)-net over F4, using
- t-expansion [i] based on digital (50, 138, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(138−83, 138, 519)-Net in Base 4 — Upper bound on s
There is no (55, 138, 520)-net in base 4, because
- 1 times m-reduction [i] would yield (55, 137, 520)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 30635 488913 334687 292592 148814 296243 464525 755923 856143 064961 544442 796217 186870 538048 > 4137 [i]