MinT - Best Known (15, 61, s)-Nets in Base 7

Best Known (15, 61, s)-Nets in Base 7

(15, 61, 23)-Net over F₇ — Constructive and digital

Digital (15, 61, 23)-net over F₇, using

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

(15, 61, 48)-Net over F₇ — Digital

Digital (15, 61, 48)-net over F₇, using

t-expansion [i] based on digital (13, 61, 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, 61, 255)-Net in Base 7 — Upper bound on s

There is no (15, 61, 256)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶¹, 256, S₇, 46), but
- the linear programming bound shows that MÂ â‰¥ 44943 151113 737152 745130 269013 948428 030303 495200 049587 751835 035356 870358 489176 511511 124246 423786 383398 237691 534450 475008 / 12 320577 740929 912102 818134 664500 489659 528092 742361 044534 286107 905247 > 7⁶¹ [i]