MinT - Best Known (63−39, 63, s)-Nets in Base 3

Best Known (63−39, 63, s)-Nets in Base 3

(63−39, 63, 32)-Net over F₃ — Constructive and digital

Digital (24, 63, 32)-net over F₃, using

t-expansion [i] based on digital (21, 63, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(63−39, 63, 109)-Net in Base 3 — Upper bound on s

There is no (24, 63, 110)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶³, 110, S₃, 39), but
- the linear programming bound shows that MÂ â‰¥ 401 475818 140604 282392 040969 710232 145438 658389 807791 365215 582135 475407 151345 717325 294327 153062 902549 711657 673773 152251 547301 / 325 455230 806957 608121 722211 436046 187202 554897 940196 290012 728886 526860 582095 622224 001861 980520 > 3⁶³ [i]