MinT - Best Known (74, 74+126, s)-Nets in Base 4

Best Known (74, 74+126, s)-Nets in Base 4

(74, 74+126, 104)-Net over F₄ — Constructive and digital

Digital (74, 200, 104)-net over F₄, using

t-expansion [i] based on digital (73, 200, 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+126, 112)-Net over F₄ — Digital

Digital (74, 200, 112)-net over F₄, using

t-expansion [i] based on digital (73, 200, 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+126, 609)-Net in Base 4 — Upper bound on s

There is no (74, 200, 610)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 590102 459107 264349 100379 422604 516688 069740 451906 465925 199487 220299 566238 091133 517006 817963 016368 810185 005073 406620 836640 > 4²⁰⁰ [i]