Best Known (228−50, 228, s)-Nets in Base 3
(228−50, 228, 688)-Net over F3 — Constructive and digital
Digital (178, 228, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(228−50, 228, 1610)-Net over F3 — Digital
Digital (178, 228, 1610)-net over F3, using
(228−50, 228, 114247)-Net in Base 3 — Upper bound on s
There is no (178, 228, 114248)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 6 076412 150189 650862 024698 132591 165705 211122 383735 460415 237930 984735 528604 459165 214322 154962 658779 135193 197841 > 3228 [i]