Best Known (165−43, 165, s)-Nets in Base 3
(165−43, 165, 288)-Net over F3 — Constructive and digital
Digital (122, 165, 288)-net over F3, using
- t-expansion [i] based on digital (121, 165, 288)-net over F3, using
- trace code for nets [i] based on digital (11, 55, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- trace code for nets [i] based on digital (11, 55, 96)-net over F27, using
(165−43, 165, 619)-Net over F3 — Digital
Digital (122, 165, 619)-net over F3, using
(165−43, 165, 23076)-Net in Base 3 — Upper bound on s
There is no (122, 165, 23077)-net in base 3, because
- 1 times m-reduction [i] would yield (122, 164, 23077)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 770710 180858 428456 065034 297848 980439 873470 089960 918601 844930 643147 932030 739995 > 3164 [i]