Best Known (28, 89, s)-Nets in Base 64
(28, 89, 513)-Net over F64 — Constructive and digital
Digital (28, 89, 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, 89, 37966)-Net in Base 64 — Upper bound on s
There is no (28, 89, 37967)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 88, 37967)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 878 785177 287107 380962 173980 871944 561415 150812 662521 611907 449804 043011 995520 813640 849701 491374 150086 911310 259744 917618 889278 315421 677111 823349 787741 828001 134804 > 6488 [i]