Best Known (67−49, 67, s)-Nets in Base 7
(67−49, 67, 26)-Net over F7 — Constructive and digital
Digital (18, 67, 26)-net over F7, using
- net from sequence [i] based on digital (18, 25)-sequence over F7, using
(67−49, 67, 51)-Net over F7 — Digital
Digital (18, 67, 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
(67−49, 67, 329)-Net in Base 7 — Upper bound on s
There is no (18, 67, 330)-net in base 7, because
- 1 times m-reduction [i] would yield (18, 66, 330)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 62 953648 684543 419931 911239 055437 505693 668771 742962 869681 > 766 [i]