Best Known (84−36, 84, s)-Nets in Base 4
(84−36, 84, 130)-Net over F4 — Constructive and digital
Digital (48, 84, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 42, 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
(84−36, 84, 1609)-Net in Base 4 — Upper bound on s
There is no (48, 84, 1610)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 375 453564 473859 112423 788568 383639 118361 260228 508368 > 484 [i]