Best Known (78−57, 78, s)-Nets in Base 7
(78−57, 78, 29)-Net over F7 — Constructive and digital
Digital (21, 78, 29)-net over F7, using
- net from sequence [i] based on digital (21, 28)-sequence over F7, using
(78−57, 78, 64)-Net over F7 — Digital
Digital (21, 78, 64)-net over F7, using
- net from sequence [i] based on digital (21, 63)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 21 and N(F) ≥ 64, using
(78−57, 78, 379)-Net in Base 7 — Upper bound on s
There is no (21, 78, 380)-net in base 7, because
- 1 times m-reduction [i] would yield (21, 77, 380)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 125291 260073 128074 269535 373138 818069 624535 228816 947877 524560 516737 > 777 [i]