MinT - Best Known (13, 13+43, s)-Nets in Base 7

Best Known (13, 13+43, s)-Nets in Base 7

(13, 13+43, 21)-Net over F₇ — Constructive and digital

Digital (13, 56, 21)-net over F₇, using

net from sequence [i] based on digital (13, 20)-sequence over F₇, using
- Niederreiter sequence [i]

(13, 13+43, 48)-Net over F₇ — Digital

Digital (13, 56, 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]

(13, 13+43, 214)-Net in Base 7 — Upper bound on s

There is no (13, 56, 215)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵⁶, 215, S₇, 43), but
- the linear programming bound shows that MÂ â‰¥ 1 488962 621741 545770 397339 272823 291858 863490 708411 604681 016011 605620 094901 524255 111902 744285 820291 037617 250034 / 6 730967 821572 051534 745282 607389 451158 475810 799606 199909 525993 > 7⁵⁶ [i]