Best Known (157−97, 157, s)-Nets in Base 4
(157−97, 157, 66)-Net over F4 — Constructive and digital
Digital (60, 157, 66)-net over F4, using
- t-expansion [i] based on digital (49, 157, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(157−97, 157, 91)-Net over F4 — Digital
Digital (60, 157, 91)-net over F4, using
- t-expansion [i] based on digital (50, 157, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(157−97, 157, 526)-Net in Base 4 — Upper bound on s
There is no (60, 157, 527)-net in base 4, because
- 1 times m-reduction [i] would yield (60, 156, 527)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 8394 371747 671725 731211 851754 888814 787131 407149 072267 720344 360025 261326 886380 908369 031832 099296 > 4156 [i]