Best Known (239−80, 239, s)-Nets in Base 3
(239−80, 239, 162)-Net over F3 — Constructive and digital
Digital (159, 239, 162)-net over F3, using
- t-expansion [i] based on digital (157, 239, 162)-net over F3, using
- 11 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
- 11 times m-reduction [i] based on digital (157, 250, 162)-net over F3, using
(239−80, 239, 367)-Net over F3 — Digital
Digital (159, 239, 367)-net over F3, using
(239−80, 239, 5552)-Net in Base 3 — Upper bound on s
There is no (159, 239, 5553)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 080025 439257 081365 523071 220269 910891 242478 724221 487771 061583 738347 775635 197482 240813 635886 697463 449261 514179 239969 > 3239 [i]