MinT - Best Known (18, 18+109, s)-Nets in Base 8

Best Known (18, 18+109, s)-Nets in Base 8

(18, 18+109, 65)-Net over F₈ — Constructive and digital

Digital (18, 127, 65)-net over F₈, using

t-expansion [i] based on digital (14, 127, 65)-net over F₈, using
- net from sequence [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]

(18, 18+109, 144)-Net in Base 8 — Upper bound on s

There is no (18, 127, 145)-net in base 8, because

3 times m-reduction [i] would yield (18, 124, 145)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹²⁴, 145, S₈, 106), but
  - the linear programming bound shows that MÂ â‰¥ 1 342408 141203 687605 592802 609181 013836 865893 869002 996708 967389 151373 449322 112488 044923 320188 176348 763972 521547 313977 170182 155517 558784 / 126 646656 585020 246257 > 8¹²⁴ [i]