MinT - Best Known (12, 53, s)-Nets in Base 7

Best Known (12, 53, s)-Nets in Base 7

(12, 53, 20)-Net over F₇ — Constructive and digital

Digital (12, 53, 20)-net over F₇, using

net from sequence [i] based on digital (12, 19)-sequence over F₇, using
- Niederreiter sequence [i]

(12, 53, 38)-Net over F₇ — Digital

Digital (12, 53, 38)-net over F₇, using

t-expansion [i] based on digital (9, 53, 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]

(12, 53, 197)-Net in Base 7 — Upper bound on s

There is no (12, 53, 198)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁵³, 198, S₇, 41), but
- the linear programming bound shows that MÂ â‰¥ 6 359925 567096 478733 383648 399387 889975 466432 979325 490824 112334 733681 408166 115226 402153 980629 626912 130246 811475 / 9782 873973 698128 663689 648991 142961 756832 345425 417159 347947 482023 > 7⁵³ [i]