MinT - Best Known (61−49, 61, s)-Nets in Base 8

Best Known (61−49, 61, s)-Nets in Base 8

(61−49, 61, 48)-Net over F₈ — Constructive and digital

Digital (12, 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]

(61−49, 61, 49)-Net over F₈ — Digital

Digital (12, 61, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(61−49, 61, 221)-Net in Base 8 — Upper bound on s

There is no (12, 61, 222)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁶¹, 222, S₈, 49), but
- the linear programming bound shows that MÂ â‰¥ 226 875109 876255 977300 221473 397045 486802 922272 083248 829750 450688 390437 817077 865787 063288 761926 237993 494674 915652 367475 204669 135233 482752 / 18 053190 463830 317919 407359 299926 746776 307782 995038 149019 542228 565262 993958 955429 > 8⁶¹ [i]