MinT - Best Known (12, 12+63, s)-Nets in Base 7

Best Known (12, 12+63, s)-Nets in Base 7

(12, 12+63, 20)-Net over F₇ — Constructive and digital

Digital (12, 75, 20)-net over F₇, using

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

(12, 12+63, 38)-Net over F₇ — Digital

Digital (12, 75, 38)-net over F₇, using

t-expansion [i] based on digital (9, 75, 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, 12+63, 102)-Net in Base 7 — Upper bound on s

There is no (12, 75, 103)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁷⁵, 103, S₇, 63), but
- the linear programming bound shows that MÂ â‰¥ 14 493370 809281 653955 032608 374020 797496 328565 275038 054555 988616 803301 260222 495813 845071 845131 / 5986 918071 757902 066359 823108 > 7⁷⁵ [i]