MinT - Best Known (17, 103, s)-Nets in Base 7

Best Known (17, 103, s)-Nets in Base 7

(17, 103, 25)-Net over F₇ — Constructive and digital

Digital (17, 103, 25)-net over F₇, using

net from sequence [i] based on digital (17, 24)-sequence over F₇, using
- Niederreiter sequence [i]

(17, 103, 48)-Net over F₇ — Digital

Digital (17, 103, 48)-net over F₇, using

t-expansion [i] based on digital (13, 103, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(17, 103, 128)-Net in Base 7 — Upper bound on s

There is no (17, 103, 129)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰³, 129, S₇, 86), but
- the linear programming bound shows that MÂ â‰¥ 3 190138 781166 615833 655091 460090 295132 442564 202369 294709 731769 348395 153590 391189 883630 521087 004338 952133 221219 814183 / 2442 979614 318644 070507 348775 > 7¹⁰³ [i]