MinT - Best Known (62−39, 62, s)-Nets in Base 3

Best Known (62−39, 62, s)-Nets in Base 3

(62−39, 62, 32)-Net over F₃ — Constructive and digital

Digital (23, 62, 32)-net over F₃, using

t-expansion [i] based on digital (21, 62, 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]

(62−39, 62, 98)-Net in Base 3 — Upper bound on s

There is no (23, 62, 99)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶², 99, S₃, 39), but
- the linear programming bound shows that MÂ â‰¥ 8341 316354 832968 167115 756462 681271 298651 307150 960469 759639 / 19004 191492 894766 602246 400000 > 3⁶² [i]