MinT - Best Known (11, 72, s)-Nets in Base 7

Best Known (11, 72, s)-Nets in Base 7

(11, 72, 19)-Net over F₇ — Constructive and digital

Digital (11, 72, 19)-net over F₇, using

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

(11, 72, 38)-Net over F₇ — Digital

Digital (11, 72, 38)-net over F₇, using

t-expansion [i] based on digital (9, 72, 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]

(11, 72, 89)-Net in Base 7 — Upper bound on s

There is no (11, 72, 90)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁷², 90, S₇, 61), but
- the linear programming bound shows that MÂ â‰¥ 2 221028 008501 492220 118056 387097 631041 334088 062669 518866 238541 254101 878484 168419 / 249257 926945 240960 > 7⁷² [i]