MinT - Best Known (18, 18+91, s)-Nets in Base 7

Best Known (18, 18+91, s)-Nets in Base 7

(18, 18+91, 26)-Net over F₇ — Constructive and digital

Digital (18, 109, 26)-net over F₇, using

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

(18, 18+91, 51)-Net over F₇ — Digital

Digital (18, 109, 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+91, 132)-Net in Base 7 — Upper bound on s

There is no (18, 109, 133)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰⁹, 133, S₇, 91), but
- the linear programming bound shows that MÂ â‰¥ 2 878465 171909 120349 908056 888939 907371 447506 624143 438070 256758 325267 819689 445087 207699 305347 048848 045643 640296 015301 / 19183 954700 034071 833600 > 7¹⁰⁹ [i]