Best Known (71, 108, s)-Nets in Base 7
(71, 108, 192)-Net over F7 — Constructive and digital
Digital (71, 108, 192)-net over F7, using
- trace code for nets [i] based on digital (17, 54, 96)-net over F49, using
- net from sequence [i] based on digital (17, 95)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- F4 from the tower of function fields by GarcÃa, Stichtenoth, and Rück over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- net from sequence [i] based on digital (17, 95)-sequence over F49, using
(71, 108, 834)-Net over F7 — Digital
Digital (71, 108, 834)-net over F7, using
(71, 108, 132916)-Net in Base 7 — Upper bound on s
There is no (71, 108, 132917)-net in base 7, because
- 1 times m-reduction [i] would yield (71, 107, 132917)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2 663835 124437 289539 701512 224695 214195 710047 534991 766907 886469 273897 738203 256653 005119 209785 > 7107 [i]