MinT - Best Known (74−62, 74, s)-Nets in Base 7

Best Known (74−62, 74, s)-Nets in Base 7

(74−62, 74, 20)-Net over F₇ — Constructive and digital

Digital (12, 74, 20)-net over F₇, using

net from sequence [i] based on digital (12, 19)-sequence over F₇, using
- Niederreiter sequence [i]

(74−62, 74, 38)-Net over F₇ — Digital

Digital (12, 74, 38)-net over F₇, using

t-expansion [i] based on digital (9, 74, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(74−62, 74, 111)-Net in Base 7 — Upper bound on s

There is no (12, 74, 112)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁷⁴, 112, S₇, 62), but
- the linear programming bound shows that MÂ â‰¥ 323 023705 901868 326618 060630 697417 174001 339767 969424 900292 735271 338809 195763 088795 682895 480156 241591 788493 327335 / 906890 224630 673356 794926 540051 067157 304375 029584 > 7⁷⁴ [i]