MinT - Best Known (74, 74+160, s)-Nets in Base 4

Best Known (74, 74+160, s)-Nets in Base 4

(74, 74+160, 104)-Net over F₄ — Constructive and digital

Digital (74, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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+160, 112)-Net over F₄ — Digital

Digital (74, 234, 112)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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+160, 524)-Net in Base 4 — Upper bound on s

There is no (74, 234, 525)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 783 158439 556324 942454 426292 087757 555841 800692 562316 125289 785465 133610 051974 190076 340805 536230 548224 342196 436244 512485 429302 898381 710044 307104 > 4²³⁴ [i]