Best Known (103−45, 103, s)-Nets in Base 4
(103−45, 103, 130)-Net over F4 — Constructive and digital
Digital (58, 103, 130)-net over F4, using
- 1 times m-reduction [i] based on digital (58, 104, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 52, 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, 52, 65)-net over F16, using
(103−45, 103, 1849)-Net in Base 4 — Upper bound on s
There is no (58, 103, 1850)-net in base 4, because
- 1 times m-reduction [i] would yield (58, 102, 1850)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 26 001897 807520 604432 810377 744846 221005 753541 947387 860051 028356 > 4102 [i]