MinT - Best Known (20, 96, s)-Nets in Base 7

Best Known (20, 96, s)-Nets in Base 7

Digital (20, 96, 28)-net over F₇, using

Digital (20, 96, 54)-net over F₇, using

t-expansion [i] based on digital (19, 96, 54)-net over F₇, using
- net from sequence [i] based on digital (19, 53)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
    - an algebraic function field by Teo [i]

There is no (20, 96, 299)-net in base 7, because

4 times m-reduction [i] would yield (20, 92, 299)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7⁹², 299, S₇, 72), but
  - 1 times code embedding in larger space [i] would yield OA(7⁹³, 300, S₇, 72), but
    - the linear programming bound shows that MÂ â‰¥ 728384 102664 463869 547718 665664 627862 412495 059558 357444 212261 856556 479386 872482 923282 511608 929845 445585 107759 983247 397759 362268 325695 250986 990071 338104 009005 903512 051476 004695 032459 428946 096948 171552 108391 892783 325188 733095 088054 724451 810208 000000 / 147971 862268 209097 126722 220347 755161 647890 710655 411438 128353 310669 205076 890596 319870 047827 172179 911400 512911 825089 867664 506375 310455 210207 145195 926708 884674 858215 688069 > 7⁹³ [i]