Best Known (161, 161+87, s)-Nets in Base 3
(161, 161+87, 162)-Net over F3 — Constructive and digital
Digital (161, 248, 162)-net over F3, using
- t-expansion [i] based on digital (157, 248, 162)-net over F3, using
- 2 times m-reduction [i] based on digital (157, 250, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F9, using
- 2 times m-reduction [i] based on digital (157, 250, 162)-net over F3, using
(161, 161+87, 329)-Net over F3 — Digital
Digital (161, 248, 329)-net over F3, using
(161, 161+87, 4604)-Net in Base 3 — Upper bound on s
There is no (161, 248, 4605)-net in base 3, because
- 1 times m-reduction [i] would yield (161, 247, 4605)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7127 357325 103316 873427 762404 325998 235155 503072 847211 517656 822200 370182 000683 702028 965116 003926 063708 662972 539985 887147 > 3247 [i]