Best Known (78−45, 78, s)-Nets in Base 7
(78−45, 78, 35)-Net over F7 — Constructive and digital
Digital (33, 78, 35)-net over F7, using
- net from sequence [i] based on digital (33, 34)-sequence over F7, using
(78−45, 78, 96)-Net over F7 — Digital
Digital (33, 78, 96)-net over F7, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
(78−45, 78, 1355)-Net in Base 7 — Upper bound on s
There is no (33, 78, 1356)-net in base 7, because
- 1 times m-reduction [i] would yield (33, 77, 1356)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 119466 489619 381167 522122 894930 413360 474116 864436 911351 792684 687337 > 777 [i]