MinT - Best Known (18, 18+89, s)-Nets in Base 7

Best Known (18, 18+89, s)-Nets in Base 7

(18, 18+89, 26)-Net over F₇ — Constructive and digital

Digital (18, 107, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(18, 18+89, 51)-Net over F₇ — Digital

Digital (18, 107, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(18, 18+89, 138)-Net in Base 7 — Upper bound on s

There is no (18, 107, 139)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰⁷, 139, S₇, 89), but
- the linear programming bound shows that MÂ â‰¥ 862080 025230 419856 632269 021355 394647 895057 556840 618631 538059 882178 178522 212684 288412 456748 423895 330272 156793 249746 516692 912219 / 289031 882246 646903 904066 733411 920000 > 7¹⁰⁷ [i]