MinT - Best Known (24, 24+44, s)-Nets in Base 3

Best Known (24, 24+44, s)-Nets in Base 3

(24, 24+44, 32)-Net over F₃ — Constructive and digital

Digital (24, 68, 32)-net over F₃, using

t-expansion [i] based on digital (21, 68, 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]

(24, 24+44, 88)-Net in Base 3 — Upper bound on s

There is no (24, 68, 89)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁸, 89, S₃, 44), but
- the linear programming bound shows that MÂ â‰¥ 382869 271658 659016 501421 251365 993917 662001 / 1091 802985 > 3⁶⁸ [i]