MinT - Best Known (98−49, 98, s)-Nets in Base 8

Best Known (98−49, 98, s)-Nets in Base 8

(98−49, 98, 130)-Net over F₈ — Constructive and digital

Digital (49, 98, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 49, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(98−49, 98, 172)-Net over F₈ — Digital

Digital (49, 98, 172)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−49, 98, 6240)-Net in Base 8 — Upper bound on s

There is no (49, 98, 6241)-net in base 8, because

1 times m-reduction [i] would yield (49, 97, 6241)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3986 866380 679876 967293 991547 803157 945756 840782 679270 759370 461813 421340 185028 350393 910468 > 8⁹⁷ [i]