MinT - Best Known (13, 13+42, s)-Nets in Base 7

Best Known (13, 13+42, s)-Nets in Base 7

(13, 13+42, 21)-Net over F₇ — Constructive and digital

Digital (13, 55, 21)-net over F₇, using

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

(13, 13+42, 48)-Net over F₇ — Digital

Digital (13, 55, 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+42, 219)-Net in Base 7 — Upper bound on s

There is no (13, 55, 220)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵⁵, 220, S₇, 42), but
- the linear programming bound shows that MÂ â‰¥ 31 803577 569886 506919 445362 102828 212262 626356 674302 033878 806744 612664 857650 795288 630002 213070 327267 327360 / 1045 810749 559495 442936 757538 395832 250252 412586 401271 063043 > 7⁵⁵ [i]