Best Known (73−61, 73, s)-Nets in Base 128
(73−61, 73, 288)-Net over F128 — Constructive and digital
Digital (12, 73, 288)-net over F128, using
- t-expansion [i] based on digital (9, 73, 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
(73−61, 73, 321)-Net over F128 — Digital
Digital (12, 73, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(73−61, 73, 10806)-Net in Base 128 — Upper bound on s
There is no (12, 73, 10807)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 72, 10807)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 52 402899 426933 307593 703161 160011 205819 662730 090841 331606 856982 524890 128740 250370 544644 307981 769093 417919 391063 649509 739945 005878 005809 231251 892892 614740 > 12872 [i]