Best Known (8, 8+∞, s)-Nets in Base 8
(8, 8+∞, 35)-Net over F8 — Constructive and digital
Digital (8, m, 35)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
(8, 8+∞, 73)-Net in Base 8 — Upper bound on s
There is no (8, m, 74)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (8, 144, 74)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8144, 74, S8, 2, 136), but
- the LP bound with quadratic polynomials shows that M ≥ 1 558240 368095 897951 083068 771488 413041 331277 636361 208915 245809 524305 417174 986761 600148 465616 230526 442890 733860 560308 807367 883476 697088 / 137 > 8144 [i]
- extracting embedded OOA [i] would yield OOA(8144, 74, S8, 2, 136), but