MinT - Best Known (126−115, 126, s)-Nets in Base 4

Best Known (126−115, 126, s)-Nets in Base 4

(126−115, 126, 27)-Net over F₄ — Constructive and digital

Digital (11, 126, 27)-net over F₄, using

t-expansion [i] based on digital (10, 126, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(126−115, 126, 45)-Net in Base 4 — Upper bound on s

There is no (11, 126, 46)-net in base 4, because

38 times m-reduction [i] would yield (11, 88, 46)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁸⁸, 46, S₄, 2, 77), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 532495 540865 888858 358347 027150 309183 618739 122183 602176 / 13 > 4⁸⁸ [i]