Best Known (145, 145+78, s)-Nets in Base 3
(145, 145+78, 162)-Net over F3 — Constructive and digital
Digital (145, 223, 162)-net over F3, using
- 3 times m-reduction [i] based on digital (145, 226, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 113, 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, 113, 81)-net over F9, using
(145, 145+78, 302)-Net over F3 — Digital
Digital (145, 223, 302)-net over F3, using
(145, 145+78, 4078)-Net in Base 3 — Upper bound on s
There is no (145, 223, 4079)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25158 238792 716304 513174 444524 720824 998435 400061 080580 496206 441443 917455 612495 684545 352951 692898 471107 422323 > 3223 [i]