Best Known (49−37, 49, s)-Nets in Base 7
(49−37, 49, 20)-Net over F7 — Constructive and digital
Digital (12, 49, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(49−37, 49, 38)-Net over F7 — Digital
Digital (12, 49, 38)-net over F7, using
- t-expansion [i] based on digital (9, 49, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(49−37, 49, 214)-Net in Base 7 — Upper bound on s
There is no (12, 49, 215)-net in base 7, because
- 1 times m-reduction [i] would yield (12, 48, 215)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 38472 796365 947463 448605 394194 110877 003013 > 748 [i]