Best Known (89−71, 89, s)-Nets in Base 7
(89−71, 89, 26)-Net over F7 — Constructive and digital
Digital (18, 89, 26)-net over F7, using
- net from sequence [i] based on digital (18, 25)-sequence over F7, using
(89−71, 89, 51)-Net over F7 — Digital
Digital (18, 89, 51)-net over F7, using
- net from sequence [i] based on digital (18, 50)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 18 and N(F) ≥ 51, using
(89−71, 89, 286)-Net in Base 7 — Upper bound on s
There is no (18, 89, 287)-net in base 7, because
- 1 times m-reduction [i] would yield (18, 88, 287)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 242 606044 629490 404351 010627 373589 873825 461068 482454 159076 625783 940993 613359 > 788 [i]