MinT - Best Known (100−49, 100, s)-Nets in Base 8

Best Known (100−49, 100, s)-Nets in Base 8

(100−49, 100, 160)-Net over F₈ — Constructive and digital

Digital (51, 100, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 50, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(100−49, 100, 190)-Net over F₈ — Digital

Digital (51, 100, 190)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−49, 100, 7424)-Net in Base 8 — Upper bound on s

There is no (51, 100, 7425)-net in base 8, because

1 times m-reduction [i] would yield (51, 99, 7425)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 255437 519990 749385 069646 452056 165064 618764 479445 792641 271345 297145 971699 213352 267910 055456 > 8⁹⁹ [i]