Best Known (54, 105, s)-Nets in Base 8
(54, 105, 160)-Net over F8 — Constructive and digital
Digital (54, 105, 160)-net over F8, using
- 1 times m-reduction [i] based on digital (54, 106, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 53, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 53, 80)-net over F64, using
(54, 105, 205)-Net over F8 — Digital
Digital (54, 105, 205)-net over F8, using
(54, 105, 8290)-Net in Base 8 — Upper bound on s
There is no (54, 105, 8291)-net in base 8, because
- 1 times m-reduction [i] would yield (54, 104, 8291)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 8362 548137 221138 871718 127907 519091 102340 822823 334784 320522 562779 517957 841461 253573 455526 867160 > 8104 [i]