MinT - Best Known (104−87, 104, s)-Nets in Base 7

Best Known (104−87, 104, s)-Nets in Base 7

(104−87, 104, 25)-Net over F₇ — Constructive and digital

Digital (17, 104, 25)-net over F₇, using

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

(104−87, 104, 48)-Net over F₇ — Digital

Digital (17, 104, 48)-net over F₇, using

t-expansion [i] based on digital (13, 104, 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]

(104−87, 104, 126)-Net in Base 7 — Upper bound on s

There is no (17, 104, 127)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰⁴, 127, S₇, 87), but
- the linear programming bound shows that MÂ â‰¥ 1215 913508 630565 553425 615169 017308 000948 884107 239469 341451 437690 220523 773012 453088 134783 403141 793824 088256 805831 / 153695 262479 768552 857600 > 7¹⁰⁴ [i]