Best Known (216−72, 216, s)-Nets in Base 3
(216−72, 216, 162)-Net over F3 — Constructive and digital
Digital (144, 216, 162)-net over F3, using
- 8 times m-reduction [i] based on digital (144, 224, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 112, 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, 112, 81)-net over F9, using
(216−72, 216, 340)-Net over F3 — Digital
Digital (144, 216, 340)-net over F3, using
(216−72, 216, 5169)-Net in Base 3 — Upper bound on s
There is no (144, 216, 5170)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 452237 284240 793618 604999 388384 809808 040188 223449 265192 350718 736465 731352 581233 748097 410176 424756 252265 > 3216 [i]