Best Known (253−88, 253, s)-Nets in Base 4
(253−88, 253, 200)-Net over F4 — Constructive and digital
Digital (165, 253, 200)-net over F4, using
- t-expansion [i] based on digital (161, 253, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(253−88, 253, 240)-Net in Base 4 — Constructive
(165, 253, 240)-net in base 4, using
- 3 times m-reduction [i] based on (165, 256, 240)-net in base 4, using
- trace code for nets [i] based on (37, 128, 120)-net in base 16, using
- 2 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- 2 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- trace code for nets [i] based on (37, 128, 120)-net in base 16, using
(253−88, 253, 582)-Net over F4 — Digital
Digital (165, 253, 582)-net over F4, using
(253−88, 253, 16622)-Net in Base 4 — Upper bound on s
There is no (165, 253, 16623)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 209 626130 129854 652299 988607 788443 742712 410510 910867 480050 818759 934695 246796 401251 421256 480621 355135 119432 973185 517600 650992 870212 266902 145416 805592 473521 > 4253 [i]