Best Known (104−56, 104, s)-Nets in Base 16
(104−56, 104, 243)-Net over F16 — Constructive and digital
Digital (48, 104, 243)-net over F16, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
(104−56, 104, 256)-Net over F16 — Digital
Digital (48, 104, 256)-net over F16, using
(104−56, 104, 257)-Net in Base 16
(48, 104, 257)-net in base 16, using
- 4 times m-reduction [i] based on (48, 108, 257)-net in base 16, using
- base change [i] based on digital (12, 72, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 72, 257)-net over F64, using
(104−56, 104, 22338)-Net in Base 16 — Upper bound on s
There is no (48, 104, 22339)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 169261 953080 149151 326800 150904 731475 847580 228202 071883 963376 467184 722295 771808 978709 550790 320076 334064 797591 195220 091938 838256 > 16104 [i]