Best Known (246−91, 246, s)-Nets in Base 3
(246−91, 246, 162)-Net over F3 — Constructive and digital
Digital (155, 246, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 123, 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
(246−91, 246, 281)-Net over F3 — Digital
Digital (155, 246, 281)-net over F3, using
(246−91, 246, 3445)-Net in Base 3 — Upper bound on s
There is no (155, 246, 3446)-net in base 3, because
- 1 times m-reduction [i] would yield (155, 245, 3446)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 789 160034 920698 980819 089271 487425 582622 423913 193090 114382 040649 383812 541584 549121 347933 609475 022556 765841 969046 098677 > 3245 [i]