Best Known (91, 138, s)-Nets in Base 3
(91, 138, 156)-Net over F3 — Constructive and digital
Digital (91, 138, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 69, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the 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) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(91, 138, 219)-Net over F3 — Digital
Digital (91, 138, 219)-net over F3, using
(91, 138, 3254)-Net in Base 3 — Upper bound on s
There is no (91, 138, 3255)-net in base 3, because
- 1 times m-reduction [i] would yield (91, 137, 3255)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 233604 616562 426629 946580 760672 071362 212392 462337 231827 651078 362931 > 3137 [i]