Best Known (138−75, 138, s)-Nets in Base 9
(138−75, 138, 128)-Net over F9 — Constructive and digital
Digital (63, 138, 128)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (13, 50, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (13, 88, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9 (see above)
- digital (13, 50, 64)-net over F9, using
(138−75, 138, 192)-Net over F9 — Digital
Digital (63, 138, 192)-net over F9, using
- t-expansion [i] based on digital (61, 138, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(138−75, 138, 6230)-Net in Base 9 — Upper bound on s
There is no (63, 138, 6231)-net in base 9, because
- 1 times m-reduction [i] would yield (63, 137, 6231)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 54001 861603 631004 575481 986407 379008 920724 651566 259696 980942 574701 853283 758923 046577 638223 795764 514894 551264 245248 213305 912659 830425 > 9137 [i]