Best Known (131, 131+98, s)-Nets in Base 4
(131, 131+98, 130)-Net over F4 — Constructive and digital
Digital (131, 229, 130)-net over F4, using
- t-expansion [i] based on digital (105, 229, 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
(131, 131+98, 265)-Net over F4 — Digital
Digital (131, 229, 265)-net over F4, using
(131, 131+98, 4108)-Net in Base 4 — Upper bound on s
There is no (131, 229, 4109)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 749909 569722 808270 635416 838333 641913 072069 819185 436812 846108 787204 456931 639367 221196 838048 210922 487544 979548 074330 958210 767320 036695 648256 > 4229 [i]