Best Known (165−54, 165, s)-Nets in Base 8
(165−54, 165, 1026)-Net over F8 — Constructive and digital
Digital (111, 165, 1026)-net over F8, using
- 1 times m-reduction [i] based on digital (111, 166, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 83, 513)-net over F64, using
(165−54, 165, 1933)-Net over F8 — Digital
Digital (111, 165, 1933)-net over F8, using
(165−54, 165, 515439)-Net in Base 8 — Upper bound on s
There is no (111, 165, 515440)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 102295 602433 693562 383421 472862 543191 820076 212740 085199 831112 451110 666160 647294 518935 827300 507909 748862 299228 065896 349582 912549 677705 785732 245092 798922 > 8165 [i]