MinT - Best Known (8, 8+158, s)-Nets in Base 8

Best Known (8, 8+158, s)-Nets in Base 8

(8, 8+158, 35)-Net over F₈ — Constructive and digital

Digital (8, 166, 35)-net over F₈, using

net from sequence [i] based on digital (8, 34)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 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 SÃ©mirat [i]

(8, 8+158, 73)-Net in Base 8 — Upper bound on s

There is no (8, 166, 74)-net in base 8, because

22 times 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 MÂ â‰¥ 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]