MinT - Best Known (43−27, 43, s)-Nets in Base 3

Best Known (43−27, 43, s)-Nets in Base 3

(43−27, 43, 28)-Net over F₃ — Constructive and digital

Digital (16, 43, 28)-net over F₃, using

t-expansion [i] based on digital (15, 43, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(43−27, 43, 84)-Net in Base 3 — Upper bound on s

There is no (16, 43, 85)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴³, 85, S₃, 27), but
- the linear programming bound shows that MÂ â‰¥ 170599 265907 526765 023977 598510 534330 288710 585034 464881 659157 890015 109721 065094 727872 297058 659726 230240 141485 607643 899814 004487 777567 313448 / 504 863183 340437 077596 773749 465604 895464 718034 015596 504179 676636 682087 511752 992455 260607 844877 228818 173806 060782 627227 > 3⁴³ [i]