Best Known (74, 74+62, s)-Nets in Base 4
(74, 74+62, 130)-Net over F4 — Constructive and digital
Digital (74, 136, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 68, 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
(74, 74+62, 138)-Net over F4 — Digital
Digital (74, 136, 138)-net over F4, using
(74, 74+62, 1787)-Net in Base 4 — Upper bound on s
There is no (74, 136, 1788)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7718 652306 175780 913431 786112 249913 355956 169705 532177 695832 076330 493577 015228 226760 > 4136 [i]