MinT - Best Known (13, 13+49, s)-Nets in Base 7

Best Known (13, 13+49, s)-Nets in Base 7

(13, 13+49, 21)-Net over F₇ — Constructive and digital

Digital (13, 62, 21)-net over F₇, using

net from sequence [i] based on digital (13, 20)-sequence over F₇, using
- Niederreiter sequence [i]

(13, 13+49, 48)-Net over F₇ — Digital

Digital (13, 62, 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]

(13, 13+49, 194)-Net in Base 7 — Upper bound on s

There is no (13, 62, 195)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁶², 195, S₇, 49), but
- the linear programming bound shows that MÂ â‰¥ 5291 576046 663346 590866 196152 243324 447656 988535 698032 473676 252180 763343 342338 293279 115105 137574 711202 449557 088217 821372 607992 791950 661875 / 198630 773144 981501 337634 545139 508514 884319 228015 874933 180629 726030 107987 592690 819013 > 7⁶² [i]