Best Known (88, 88+157, s)-Nets in Base 4
(88, 88+157, 104)-Net over F4 — Constructive and digital
Digital (88, 245, 104)-net over F4, using
- t-expansion [i] based on digital (73, 245, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(88, 88+157, 129)-Net over F4 — Digital
Digital (88, 245, 129)-net over F4, using
- t-expansion [i] based on digital (81, 245, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(88, 88+157, 698)-Net in Base 4 — Upper bound on s
There is no (88, 245, 699)-net in base 4, because
- 1 times m-reduction [i] would yield (88, 244, 699)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 854 859123 759562 327334 603794 816097 933728 888992 091784 914040 704330 637693 024089 620415 564226 208724 972575 180864 875271 739838 077129 575464 425466 924463 029080 > 4244 [i]