Best Known (46, 93, s)-Nets in Base 7
(46, 93, 50)-Net over F7 — Constructive and digital
Digital (46, 93, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(46,49) in PG(92,7)) for nets [i] based on digital (0, 47, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
(46, 93, 136)-Net over F7 — Digital
Digital (46, 93, 136)-net over F7, using
(46, 93, 3758)-Net in Base 7 — Upper bound on s
There is no (46, 93, 3759)-net in base 7, because
- 1 times m-reduction [i] would yield (46, 92, 3759)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 563555 838503 776668 225662 293910 963110 152880 148321 398902 370821 349846 641464 458999 > 792 [i]