Best Known (99, 186, s)-Nets in Base 4
(99, 186, 130)-Net over F4 — Constructive and digital
Digital (99, 186, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 93, 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
(99, 186, 166)-Net over F4 — Digital
Digital (99, 186, 166)-net over F4, using
(99, 186, 2155)-Net in Base 4 — Upper bound on s
There is no (99, 186, 2156)-net in base 4, because
- 1 times m-reduction [i] would yield (99, 185, 2156)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2419 278661 034689 233334 575697 387131 214347 616704 132037 636210 802746 264689 850828 829833 487840 944123 914770 959729 218169 > 4185 [i]