Best Known (90, 145, s)-Nets in Base 4
(90, 145, 130)-Net over F4 — Constructive and digital
Digital (90, 145, 130)-net over F4, using
- 23 times m-reduction [i] based on digital (90, 168, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 84, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 84, 65)-net over F16, using
(90, 145, 267)-Net over F4 — Digital
Digital (90, 145, 267)-net over F4, using
(90, 145, 5897)-Net in Base 4 — Upper bound on s
There is no (90, 145, 5898)-net in base 4, because
- 1 times m-reduction [i] would yield (90, 144, 5898)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 498 786792 816986 220932 005043 001606 454653 101698 818852 595868 439553 275835 284531 665006 657152 > 4144 [i]