Best Known (74, 74+73, s)-Nets in Base 9
(74, 74+73, 165)-Net over F9 — Constructive and digital
Digital (74, 147, 165)-net over F9, using
- t-expansion [i] based on digital (64, 147, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(74, 74+73, 280)-Net over F9 — Digital
Digital (74, 147, 280)-net over F9, using
(74, 74+73, 13210)-Net in Base 9 — Upper bound on s
There is no (74, 147, 13211)-net in base 9, because
- 1 times m-reduction [i] would yield (74, 146, 13211)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 20 911775 768914 725039 090673 198022 316214 471697 434403 261276 266194 438033 934820 170048 781915 471469 263487 884970 839981 590896 984622 698434 727644 167521 > 9146 [i]