MinT - Best Known (10, 10+56, s)-Nets in Base 7

Best Known (10, 10+56, s)-Nets in Base 7

(10, 10+56, 18)-Net over F₇ — Constructive and digital

Digital (10, 66, 18)-net over F₇, using

net from sequence [i] based on digital (10, 17)-sequence over F₇, using
- Niederreiter sequence [i]

(10, 10+56, 38)-Net over F₇ — Digital

Digital (10, 66, 38)-net over F₇, using

t-expansion [i] based on digital (9, 66, 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]

(10, 10+56, 85)-Net in Base 7 — Upper bound on s

There is no (10, 66, 86)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶⁶, 86, S₇, 56), but
- the linear programming bound shows that MÂ â‰¥ 1 334231 573915 578008 357714 345358 859196 523515 546179 070417 602152 297419 380813 / 18468 973862 798877 > 7⁶⁶ [i]