Best Known (76−42, 76, s)-Nets in Base 64
(76−42, 76, 513)-Net over F64 — Constructive and digital
Digital (34, 76, 513)-net over F64, using
- t-expansion [i] based on digital (28, 76, 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
(76−42, 76, 592)-Net over F64 — Digital
Digital (34, 76, 592)-net over F64, using
(76−42, 76, 474016)-Net in Base 64 — Upper bound on s
There is no (34, 76, 474017)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 186071 005207 041396 023300 481485 729519 374889 776592 953356 978079 694674 648838 894146 406758 360234 507891 552595 537139 815767 237855 426842 766606 230688 > 6476 [i]