Best Known (242−62, 242, s)-Nets in Base 3
(242−62, 242, 324)-Net over F3 — Constructive and digital
Digital (180, 242, 324)-net over F3, using
- 1 times m-reduction [i] based on digital (180, 243, 324)-net over F3, using
- trace code for nets [i] based on digital (18, 81, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- trace code for nets [i] based on digital (18, 81, 108)-net over F27, using
(242−62, 242, 906)-Net over F3 — Digital
Digital (180, 242, 906)-net over F3, using
(242−62, 242, 32902)-Net in Base 3 — Upper bound on s
There is no (180, 242, 32903)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 085584 306522 993980 422370 360568 308078 187581 662817 602490 272324 537090 083398 810341 948686 546858 576815 706628 307765 570275 > 3242 [i]