MinT - Best Known (75−67, 75, s)-Nets in Base 4

Best Known (75−67, 75, s)-Nets in Base 4

(75−67, 75, 21)-Net over F₄ — Constructive and digital

Digital (8, 75, 21)-net over F₄, using

t-expansion [i] based on digital (7, 75, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(75−67, 75, 35)-Net in Base 4 — Upper bound on s

There is no (8, 75, 36)-net in base 4, because

7 times m-reduction [i] would yield (8, 68, 36)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4⁶⁸, 36, S₄, 2, 60), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 5 575186 299632 655785 383929 568162 090376 495104 / 61 > 4⁶⁸ [i]