MinT - Best Known (61−48, 61, s)-Nets in Base 8

Best Known (61−48, 61, s)-Nets in Base 8

(61−48, 61, 48)-Net over F₈ — Constructive and digital

Digital (13, 61, 48)-net over F₈, using

t-expansion [i] based on digital (11, 61, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(61−48, 61, 56)-Net over F₈ — Digital

Digital (13, 61, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(61−48, 61, 249)-Net in Base 8 — Upper bound on s

There is no (13, 61, 250)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶¹, 250, S₈, 48), but
- the linear programming bound shows that MÂ â‰¥ 27 698338 677761 294017 318463 087546 189657 065687 295627 413131 457925 426086 508853 254815 465870 474392 005014 685141 721663 638505 186396 209152 / 2 143706 733954 845366 289529 413491 164398 886769 971666 461069 935848 636313 067819 > 8⁶¹ [i]