Best Known (93, 174, s)-Nets in Base 4
(93, 174, 130)-Net over F4 — Constructive and digital
Digital (93, 174, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 87, 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
(93, 174, 159)-Net over F4 — Digital
Digital (93, 174, 159)-net over F4, using
(93, 174, 2078)-Net in Base 4 — Upper bound on s
There is no (93, 174, 2079)-net in base 4, because
- 1 times m-reduction [i] would yield (93, 173, 2079)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 143 877866 371666 658150 739301 324741 631701 088974 813363 900099 604934 570466 462067 801118 883706 538812 041278 505792 > 4173 [i]