Best Known (60−45, 60, s)-Nets in Base 128
(60−45, 60, 288)-Net over F128 — Constructive and digital
Digital (15, 60, 288)-net over F128, using
- t-expansion [i] based on digital (9, 60, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(60−45, 60, 386)-Net over F128 — Digital
Digital (15, 60, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
(60−45, 60, 31919)-Net in Base 128 — Upper bound on s
There is no (15, 60, 31920)-net in base 128, because
- 1 times m-reduction [i] would yield (15, 59, 31920)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 21158 882169 566327 728367 759547 514976 959809 525009 293220 054939 969478 021285 225932 933599 628918 380427 141839 270268 578990 436997 549818 > 12859 [i]