Best Known (85−56, 85, s)-Nets in Base 64
(85−56, 85, 513)-Net over F64 — Constructive and digital
Digital (29, 85, 513)-net over F64, using
- t-expansion [i] based on digital (28, 85, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(85−56, 85, 54525)-Net in Base 64 — Upper bound on s
There is no (29, 85, 54526)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3352 785413 346791 981732 359821 270203 337953 525387 586460 316140 882670 272212 415344 920499 035667 961901 362759 972095 703781 207028 295288 219216 958013 733650 708993 215683 > 6485 [i]