Best Known (82, 82+39, s)-Nets in Base 4
(82, 82+39, 240)-Net over F4 — Constructive and digital
Digital (82, 121, 240)-net over F4, using
- 41 times duplication [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
(82, 82+39, 413)-Net over F4 — Digital
Digital (82, 121, 413)-net over F4, using
(82, 82+39, 16756)-Net in Base 4 — Upper bound on s
There is no (82, 121, 16757)-net in base 4, because
- 1 times m-reduction [i] would yield (82, 120, 16757)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 768002 053757 469311 924842 431462 025801 293580 050879 133859 247578 116280 139852 > 4120 [i]