Best Known (72, 110, s)-Nets in Base 7
(72, 110, 192)-Net over F7 — Constructive and digital
Digital (72, 110, 192)-net over F7, using
- trace code for nets [i] based on digital (17, 55, 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
(72, 110, 813)-Net over F7 — Digital
Digital (72, 110, 813)-net over F7, using
(72, 110, 103201)-Net in Base 7 — Upper bound on s
There is no (72, 110, 103202)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 913 747071 663926 952944 698682 293885 337997 793275 011677 037990 085750 797217 463692 533547 913458 382249 > 7110 [i]