Best Known (46, 89, s)-Nets in Base 4
(46, 89, 60)-Net over F4 — Constructive and digital
Digital (46, 89, 60)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 31, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (15, 58, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (10, 31, 27)-net over F4, using
(46, 89, 65)-Net in Base 4 — Constructive
(46, 89, 65)-net in base 4, using
- 7 times m-reduction [i] based on (46, 96, 65)-net in base 4, using
- base change [i] based on digital (14, 64, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- base change [i] based on digital (14, 64, 65)-net over F8, using
(46, 89, 82)-Net over F4 — Digital
Digital (46, 89, 82)-net over F4, using
(46, 89, 947)-Net in Base 4 — Upper bound on s
There is no (46, 89, 948)-net in base 4, because
- 1 times m-reduction [i] would yield (46, 88, 948)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 96647 812969 486870 891477 017912 098796 373890 896430 339640 > 488 [i]