MinT - Best Known (60−38, 60, s)-Nets in Base 3

Best Known (60−38, 60, s)-Nets in Base 3

(60−38, 60, 32)-Net over F₃ — Constructive and digital

Digital (22, 60, 32)-net over F₃, using

t-expansion [i] based on digital (21, 60, 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]

(60−38, 60, 93)-Net in Base 3 — Upper bound on s

There is no (22, 60, 94)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁰, 94, S₃, 38), but
- the linear programming bound shows that MÂ â‰¥ 132 944288 351905 684103 161899 822708 298724 029601 023671 / 2537 510710 702022 341000 > 3⁶⁰ [i]