MinT - Best Known (107−93, 107, s)-Nets in Base 9

Best Known (107−93, 107, s)-Nets in Base 9

(107−93, 107, 64)-Net over F₉ — Constructive and digital

Digital (14, 107, 64)-net over F₉, using

t-expansion [i] based on digital (13, 107, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(107−93, 107, 147)-Net in Base 9 — Upper bound on s

There is no (14, 107, 148)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9¹⁰⁷, 148, S₉, 93), but
- the linear programming bound shows that MÂ â‰¥ 4775 988366 769322 535267 947994 713802 793051 066875 714494 752850 033216 462585 180440 024465 722736 114808 721391 751734 913702 501109 786269 791051 552650 499673 431911 / 3756 424016 109451 407019 421049 013948 133644 014500 > 9¹⁰⁷ [i]