Best Known (24, 24+54, s)-Nets in Base 64
(24, 24+54, 177)-Net over F64 — Constructive and digital
Digital (24, 78, 177)-net over F64, using
- t-expansion [i] based on digital (7, 78, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(24, 24+54, 288)-Net in Base 64 — Constructive
(24, 78, 288)-net in base 64, using
- t-expansion [i] based on (22, 78, 288)-net in base 64, using
- 13 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 13 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(24, 24+54, 342)-Net over F64 — Digital
Digital (24, 78, 342)-net over F64, using
- t-expansion [i] based on digital (20, 78, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(24, 24+54, 28623)-Net in Base 64 — Upper bound on s
There is no (24, 78, 28624)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 834000 232960 113655 710440 085664 377849 640467 269264 679104 863554 717370 689710 988646 760537 231309 603275 040911 321039 054693 399289 988649 837848 739300 > 6478 [i]