Best Known (9, 9+31, s)-Nets in Base 49
(9, 9+31, 59)-Net over F49 — Constructive and digital
Digital (9, 40, 59)-net over F49, using
- net from sequence [i] based on digital (9, 58)-sequence over F49, using
(9, 9+31, 92)-Net over F49 — Digital
Digital (9, 40, 92)-net over F49, using
- t-expansion [i] based on digital (3, 40, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(9, 9+31, 3311)-Net in Base 49 — Upper bound on s
There is no (9, 40, 3312)-net in base 49, because
- 1 times m-reduction [i] would yield (9, 39, 3312)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 827626 206240 685084 273624 563143 331414 894939 440777 045929 904259 128065 > 4939 [i]