Best Known (112−49, 112, s)-Nets in Base 5
(112−49, 112, 132)-Net over F5 — Constructive and digital
Digital (63, 112, 132)-net over F5, using
- 6 times m-reduction [i] based on digital (63, 118, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 59, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 59, 66)-net over F25, using
(112−49, 112, 181)-Net over F5 — Digital
Digital (63, 112, 181)-net over F5, using
(112−49, 112, 4170)-Net in Base 5 — Upper bound on s
There is no (63, 112, 4171)-net in base 5, because
- 1 times m-reduction [i] would yield (63, 111, 4171)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 385543 381578 273496 271287 971949 751673 633152 349689 134282 801813 934134 776643 749025 > 5111 [i]