MinT - Best Known (16, 16+80, s)-Nets in Base 7

Best Known (16, 16+80, s)-Nets in Base 7

(16, 16+80, 24)-Net over F₇ — Constructive and digital

Digital (16, 96, 24)-net over F₇, using

net from sequence [i] based on digital (16, 23)-sequence over F₇, using
- Niederreiter sequence [i]

(16, 16+80, 48)-Net over F₇ — Digital

Digital (16, 96, 48)-net over F₇, using

t-expansion [i] based on digital (13, 96, 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]

(16, 16+80, 129)-Net in Base 7 — Upper bound on s

There is no (16, 96, 130)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7⁹⁶, 130, S₇, 80), but
- the linear programming bound shows that MÂ â‰¥ 1008 675673 708239 065449 274441 675980 467384 407621 247203 498751 244240 594753 309872 721398 739658 362512 094646 529307 652407 719481 / 585184 362066 809703 107594 592021 972000 > 7⁹⁶ [i]