Best Known (60, 60+53, s)-Nets in Base 4
(60, 60+53, 76)-Net over F4 — Constructive and digital
Digital (60, 113, 76)-net over F4, using
- 1 times m-reduction [i] based on digital (60, 114, 76)-net over F4, using
- trace code for nets [i] based on digital (3, 57, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- trace code for nets [i] based on digital (3, 57, 38)-net over F16, using
(60, 60+53, 109)-Net over F4 — Digital
Digital (60, 113, 109)-net over F4, using
(60, 60+53, 1358)-Net in Base 4 — Upper bound on s
There is no (60, 113, 1359)-net in base 4, because
- 1 times m-reduction [i] would yield (60, 112, 1359)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 27 336225 394500 544960 021013 435773 880653 992463 288490 757314 340661 557988 > 4112 [i]