Best Known (57, 57+31, s)-Nets in Base 7
(57, 57+31, 126)-Net over F7 — Constructive and digital
Digital (57, 88, 126)-net over F7, using
- trace code for nets [i] based on digital (13, 44, 63)-net over F49, using
- net from sequence [i] based on digital (13, 62)-sequence over F49, using
(57, 57+31, 620)-Net over F7 — Digital
Digital (57, 88, 620)-net over F7, using
(57, 57+31, 85336)-Net in Base 7 — Upper bound on s
There is no (57, 88, 85337)-net in base 7, because
- 1 times m-reduction [i] would yield (57, 87, 85337)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 33 385266 978516 248995 932750 893204 985284 246554 099002 663891 090707 002868 048503 > 787 [i]