Best Known (66−37, 66, s)-Nets in Base 64
(66−37, 66, 513)-Net over F64 — Constructive and digital
Digital (29, 66, 513)-net over F64, using
- t-expansion [i] based on digital (28, 66, 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
(66−37, 66, 399113)-Net in Base 64 — Upper bound on s
There is no (29, 66, 399114)-net in base 64, because
- 1 times m-reduction [i] would yield (29, 65, 399114)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 2521 774609 085566 533227 890246 813810 030303 749653 641165 305030 123086 932426 386189 870217 463529 506368 392064 814893 619497 956160 > 6465 [i]