Best Known (28, 85, s)-Nets in Base 64
(28, 85, 513)-Net over F64 — Constructive and digital
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
(28, 85, 46997)-Net in Base 64 — Upper bound on s
There is no (28, 85, 46998)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 84, 46998)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 52 387098 895114 664420 716159 539211 325740 414899 257109 500083 741511 758361 373649 072442 523935 020158 605928 882399 827840 759958 063852 627910 124474 637277 147274 000080 > 6484 [i]