MinT - Best Known (152−138, 152, s)-Nets in Base 8

Best Known (152−138, 152, s)-Nets in Base 8

(152−138, 152, 65)-Net over F₈ — Constructive and digital

Digital (14, 152, 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]

(152−138, 152, 115)-Net in Base 8 — Upper bound on s

There is no (14, 152, 116)-net in base 8, because

47 times m-reduction [i] would yield (14, 105, 116)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹⁰⁵, 116, S₈, 91), but
  - the linear programming bound shows that MÂ â‰¥ 67 590695 303585 232363 449610 385167 125134 814310 899640 912361 983716 500606 168825 384014 701443 407135 513537 150976 / 996 991281 > 8¹⁰⁵ [i]