Best Known (135, 252, s)-Nets in Base 4
(135, 252, 130)-Net over F4 — Constructive and digital
Digital (135, 252, 130)-net over F4, using
- t-expansion [i] based on digital (105, 252, 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
(135, 252, 223)-Net over F4 — Digital
Digital (135, 252, 223)-net over F4, using
(135, 252, 2969)-Net in Base 4 — Upper bound on s
There is no (135, 252, 2970)-net in base 4, because
- 1 times m-reduction [i] would yield (135, 251, 2970)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 236907 786922 880371 357408 131845 508546 946427 759757 816705 991360 532969 551804 980235 579214 449804 016092 879669 668908 975853 483739 592941 333794 445080 092961 705120 > 4251 [i]