MinT - Best Known (35, ∞, s)-Nets in Base 8

Best Known (35, ∞, s)-Nets in Base 8

Digital (35, m, 65)-net over F₈ for arbitrarily large m, using

net from sequence [i] based on digital (35, 64)-sequence over F₈, using
- t-expansion [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

Digital (35, m, 112)-net over F₈ for arbitrarily large m, using

There is no (35, m, 268)-net in base 8 for arbitrarily large m, because

m-reduction [i] would yield (35, 800, 268)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8⁸⁰⁰, 268, S₈, 3, 765), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 128077 647029 270553 940191 515853 744132 947245 818974 337596 320547 559879 936938 494810 111029 941696 247313 879284 784446 110945 113844 232979 374586 832779 015418 020713 975286 675940 242912 815237 198965 241901 618015 838019 027299 465036 267357 091264 024778 889561 469476 285107 200889 425106 158704 585162 207009 978392 340095 537030 687829 665381 549935 717841 068332 724918 191186 738770 822135 392973 429207 811839 549450 130030 070135 266938 012494 486605 102821 021680 159137 234688 884097 870141 525241 830776 344716 054735 238456 909736 770497 605430 091842 741771 980836 922559 790010 092539 066825 071532 129578 565235 256113 680416 438405 079364 166850 830890 665630 631139 631226 624021 372933 816355 262340 130458 444750 734022 496268 084503 459920 901867 346191 919656 111096 894384 995770 503274 052145 455405 176226 578432 / 383 > 8⁸⁰⁰ [i]