Best Known (163, 163+87, s)-Nets in Base 3
(163, 163+87, 162)-Net over F3 — Constructive and digital
Digital (163, 250, 162)-net over F3, using
- t-expansion [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
(163, 163+87, 339)-Net over F3 — Digital
Digital (163, 250, 339)-net over F3, using
(163, 163+87, 4847)-Net in Base 3 — Upper bound on s
There is no (163, 250, 4848)-net in base 3, because
- 1 times m-reduction [i] would yield (163, 249, 4848)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 63789 241463 223741 934179 628676 615860 114916 367723 770703 146209 936243 173278 227464 898090 119613 452670 362793 734826 506179 000769 > 3249 [i]