MinT - Best Known (15, 15+50, s)-Nets in Base 7

Best Known (15, 15+50, s)-Nets in Base 7

(15, 15+50, 23)-Net over F₇ — Constructive and digital

Digital (15, 65, 23)-net over F₇, using

net from sequence [i] based on digital (15, 22)-sequence over F₇, using
- Niederreiter sequence [i]

(15, 15+50, 48)-Net over F₇ — Digital

Digital (15, 65, 48)-net over F₇, using

t-expansion [i] based on digital (13, 65, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(15, 15+50, 240)-Net in Base 7 — Upper bound on s

There is no (15, 65, 241)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶⁵, 241, S₇, 50), but
- the linear programming bound shows that MÂ â‰¥ 22112 624364 978795 474538 754976 749930 094707 292079 021651 687603 190206 394263 161826 780561 387920 429787 399829 683425 235249 342283 395238 283264 / 2560 243716 514173 842701 937347 863769 540331 960625 883665 166806 472978 012051 423879 > 7⁶⁵ [i]