MinT - Best Known (55−44, 55, s)-Nets in Base 7

Best Known (55−44, 55, s)-Nets in Base 7

(55−44, 55, 19)-Net over F₇ — Constructive and digital

Digital (11, 55, 19)-net over F₇, using

net from sequence [i] based on digital (11, 18)-sequence over F₇, using
- Niederreiter sequence [i]

(55−44, 55, 38)-Net over F₇ — Digital

Digital (11, 55, 38)-net over F₇, using

t-expansion [i] based on digital (9, 55, 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]

(55−44, 55, 165)-Net in Base 7 — Upper bound on s

There is no (11, 55, 166)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵⁵, 166, S₇, 44), but
- the linear programming bound shows that MÂ â‰¥ 28 270368 960377 491366 112717 818905 584373 568120 154174 546471 036593 186282 256341 262578 966022 980017 498407 341165 884606 / 871 828612 247468 369137 222003 214883 045722 955809 678160 946790 887441 > 7⁵⁵ [i]