Best Known (69, 69+55, s)-Nets in Base 8
(69, 69+55, 354)-Net over F8 — Constructive and digital
Digital (69, 124, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 62, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(69, 69+55, 20277)-Net in Base 8 — Upper bound on s
There is no (69, 124, 20278)-net in base 8, because
- 1 times m-reduction [i] would yield (69, 123, 20278)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1202 496326 326120 539129 946177 571287 622037 063122 761071 687383 297364 211242 985849 521965 676082 523875 070356 278363 524040 > 8123 [i]