MinT - Best Known (50−39, 50, s)-Nets in Base 7

Best Known (50−39, 50, s)-Nets in Base 7

(50−39, 50, 19)-Net over F₇ — Constructive and digital

Digital (11, 50, 19)-net over F₇, using

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

(50−39, 50, 38)-Net over F₇ — Digital

Digital (11, 50, 38)-net over F₇, using

t-expansion [i] based on digital (9, 50, 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]

(50−39, 50, 180)-Net in Base 7 — Upper bound on s

There is no (11, 50, 181)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵⁰, 181, S₇, 39), but
- the linear programming bound shows that MÂ â‰¥ 6969 879574 456399 105177 813640 659038 908360 271523 065113 268643 530902 807072 189261 309334 447122 511495 400000 / 3611 493385 806681 349111 258806 113778 332249 667025 657892 257191 > 7⁵⁰ [i]