Best Known (78−65, 78, s)-Nets in Base 16
(78−65, 78, 65)-Net over F16 — Constructive and digital
Digital (13, 78, 65)-net over F16, using
- t-expansion [i] based on digital (6, 78, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(78−65, 78, 97)-Net over F16 — Digital
Digital (13, 78, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
(78−65, 78, 655)-Net in Base 16 — Upper bound on s
There is no (13, 78, 656)-net in base 16, because
- 1 times m-reduction [i] would yield (13, 77, 656)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 527 150095 892265 206299 542951 426039 213775 353279 041659 953434 815911 049278 722993 754858 857353 055356 > 1677 [i]