Best Known (81, 81+37, s)-Nets in Base 4
(81, 81+37, 240)-Net over F4 — Constructive and digital
Digital (81, 118, 240)-net over F4, using
- 2 times m-reduction [i] based on digital (81, 120, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 40, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 40, 80)-net over F64, using
(81, 81+37, 453)-Net over F4 — Digital
Digital (81, 118, 453)-net over F4, using
(81, 81+37, 20610)-Net in Base 4 — Upper bound on s
There is no (81, 118, 20611)-net in base 4, because
- 1 times m-reduction [i] would yield (81, 117, 20611)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 27613 458646 153044 124948 691265 578933 869425 577788 013155 761417 695681 602040 > 4117 [i]