Best Known (248−92, 248, s)-Nets in Base 3
(248−92, 248, 162)-Net over F3 — Constructive and digital
Digital (156, 248, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 124, 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
(248−92, 248, 280)-Net over F3 — Digital
Digital (156, 248, 280)-net over F3, using
(248−92, 248, 3316)-Net in Base 3 — Upper bound on s
There is no (156, 248, 3317)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21466 435596 586242 097200 327278 318771 990447 705442 562842 882178 204686 201682 311558 522348 217823 390314 093058 983591 652822 707265 > 3248 [i]