Best Known (62, 105, s)-Nets in Base 4
(62, 105, 130)-Net over F4 — Constructive and digital
Digital (62, 105, 130)-net over F4, using
- 7 times m-reduction [i] based on digital (62, 112, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 56, 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, 56, 65)-net over F16, using
(62, 105, 158)-Net over F4 — Digital
Digital (62, 105, 158)-net over F4, using
(62, 105, 2756)-Net in Base 4 — Upper bound on s
There is no (62, 105, 2757)-net in base 4, because
- 1 times m-reduction [i] would yield (62, 104, 2757)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 413 338727 061570 280688 564053 260170 283959 247770 987494 739373 240208 > 4104 [i]