Best Known (47, 47+45, s)-Nets in Base 5
(47, 47+45, 78)-Net over F5 — Constructive and digital
Digital (47, 92, 78)-net over F5, using
- t-expansion [i] based on digital (38, 92, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(47, 47+45, 105)-Net over F5 — Digital
Digital (47, 92, 105)-net over F5, using
(47, 47+45, 1745)-Net in Base 5 — Upper bound on s
There is no (47, 92, 1746)-net in base 5, because
- 1 times m-reduction [i] would yield (47, 91, 1746)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4040 175723 467653 440679 397188 468987 398703 768089 232148 979586 676225 > 591 [i]