MinT - Best Known (74, 74+166, s)-Nets in Base 4

Best Known (74, 74+166, s)-Nets in Base 4

(74, 74+166, 104)-Net over F₄ — Constructive and digital

Digital (74, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(74, 74+166, 112)-Net over F₄ — Digital

Digital (74, 240, 112)-net over F₄, using

t-expansion [i] based on digital (73, 240, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(74, 74+166, 516)-Net in Base 4 — Upper bound on s

There is no (74, 240, 517)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 471737 704497 549864 521973 999977 108426 795875 203942 410606 967551 277048 521597 402102 733754 944185 421136 821999 701479 578171 809822 523530 778572 834003 702656 > 4²⁴⁰ [i]