Best Known (68−49, 68, s)-Nets in Base 7
(68−49, 68, 27)-Net over F7 — Constructive and digital
Digital (19, 68, 27)-net over F7, using
- net from sequence [i] based on digital (19, 26)-sequence over F7, using
(68−49, 68, 54)-Net over F7 — Digital
Digital (19, 68, 54)-net over F7, using
- net from sequence [i] based on digital (19, 53)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 19 and N(F) ≥ 54, using
(68−49, 68, 358)-Net in Base 7 — Upper bound on s
There is no (19, 68, 359)-net in base 7, because
- 1 times m-reduction [i] would yield (19, 67, 359)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 436 611410 040332 010253 104978 900615 859302 959461 041670 118641 > 767 [i]